Let us read the first 8 verses of the chapter:

1 Rebuke not an elder, but intreat him as a father; and the younger men as brethren;
2 The elder women as mothers; the younger as sisters, with all purity.
3 Honour widows that are widows indeed.
4 But if any widow have children or nephews, let them learn first to shew piety at home, and to requite their parents: for that is good and acceptable before God.
5 Now she that is a widow indeed, and desolate, trusteth in God, and continueth in supplications and prayers night and day.
6 But she that liveth in pleasure is dead while she liveth.
7 And these things give in charge, that they may be blameless.
8 But if any provide not for his own, and specially for those of his own house, he hath denied the faith, and is worse than an infidel.

CHURCH AND FAMILY DUTY

Honour widows who are genuinely in a widow’s destitute position. But if any widow has children or grandchildren, let such children learn to begin by discharging the duties of religion in their own homes; and let them learn to give a return for all that their parents have done for them; for this is the kind of conduct that meets with God’s approval. Now she who is genuinely in the position of a widow, and who is left all alone, has set her hope on God, and night and day she devotes herself to petitions and prayers. But she who lives with voluptuous wantonness is dead even though she is still alive. Pass on these instructions that they may be irreproachable. If anyone fails to provide for his own people, and especially for the members of his own family, he has denied the faith and is worse than an unbeliever.

THE Christian Church inherited a fine tradition of charity to those in need. No nation has ever cared more for the needy and the elderly than the Jews. Advice is now given for the care of widows. There may well have been two classes of women here. There were certainly widows who had become widows in the normal way by the death of their husbands. But it was not uncommon in the Gentile world, in certain places, for a man to have more than one wife. When a man became a Christian, he could not go on being a polygamist, and therefore he had to choose which wife he was going to live with. That meant that some wives had to be sent away, and they were clearly in a very unfortunate position. It may be that such women as these were also considered to be widows and were given the support of the Church. Jewish law laid it down that at the time of his marriage a man ought to make provision for his wife, should she become a widow. The very first office-bearers whom the Christian Church appointed had this duty of caring fairly for the widows (Acts 6:1). Ignatius lays it down: ‘Let not widows be neglected. After the Lord be thou their guardian.’ The Apostolic Constitutions direct the bishop: ‘O bishop, be mindful of the needy, both reaching out thy helping hand and making provision for them as the steward of God, distributing the offerings seasonably to every one of them, to the widows, the orphans, the friendless, and those tried with affliction.’ The same book has an interesting and kindly instruction: ‘If anyone receives any service to carry to a widow or poor woman . . . let him give it the same day.’ As the proverb has it, ‘He gives twice who gives quickly’ – and the Church was concerned that those in poverty should not have to remain in need while one of its servants delayed.

It is to be noted that the Church did not propose to assume responsibility for older people whose children were alive and well able to support them. The ancient world was very definite that it was the duty of children to support elderly parents; and, as E. K. Simpson has pointed out in his commentary, ‘A religious profession which falls below the standard of duty recognized by the world is a wretched fraud.’ The Church would never have agreed that its charity should become an excuse for children to evade their responsibility.

The New Testament ethical writers were certain that support of parents was an essential part of Christian duty. It is something to be remembered. We live in a time when even the most sacred duties are pushed on to the state and when we expect, in so many cases, public charity to do what private piety ought to do. As the Pastorals see it, help given to a parent is two things. First, it is an honouring of the recipient. It is the only way in which children can demonstrate the esteem that they feel. Second, it is an admission of the claims of love. It is repaying love received in time of need with love given in time of need; and only with love can love be repaid.

There remains one thing left to say, and to leave it unsaid would be unfair. This passage goes on to lay down certain of the qualities of the people whom the Church is called upon to support. What is true of the Church is true within the family.  If a person is to be supported, that person must be supportable. If a parent is taken into the home of a son or daughter and then by inconsiderate conduct causes nothing but trouble, another situation arises. There is a double duty here – the duty of the child to support the parent, and the duty of the parent to behave in such a way that that support is possible within the structure of the home. ~this text from the Barclay Commentary

Now to the commentaries...

The verse is in four parts:

1] But if any provide not for his own.
2] And specially for those of his own house.
3] He hath denied the faith.
4] And is worse than an infidel.

1] But if any provide not for his own.

But if any provide not for his own - His own people or relatives.  ~Adam Clarke

But if any provide not for his own - Not only for his wife and children, but for his parents, when grown old, and cannot help themselves: ~John Gill

But if any provide not for his own - The apostle was speaking 1 Timothy 5:4 particularly of the duty of children toward a widowed mother.

1 Timothy 5:4
But if any widow have children or nephews, let them learn first to shew piety at home, and to requite their parents: for that is good and acceptable before God.

In enforcing that duty, he gives the subject, as he often does in similar cases, a general direction, and says that all ought to provide for those who were dependent on them, and that if they did not do this, they had a less impressive sense of the obligations of duty than even the pagan had. On the duty here referred to, compare Romans 12:17 note; 2 Corinthians 8:21 note. The meaning is, that the person referred to is to think beforehand (προνοεἶ pronoei) of the probable needs of his own family, and make arrangements to meet them. God thus provides for our needs; that is, he sees beforehand what we shall need, and makes arrangements for those needs by long preparation. The food that we eat, and the raiment that we wear, he foresaw that we should need, and the arrangement for the supply was made years since, and to meet these needs he has been carrying forward the plans of his providence in the seasons; in the growth of animals; in the formation of fruit; in the bountiful harvest. So, according to our measure, we are to anticipate what will be the probable needs of our families, and to make arrangements to meet them. The words “his own,” refer to those who are naturally dependent on him, whether living in his own immediate family or not. There may be many distant relatives naturally dependent on our aid, besides those who live in our own house. ~Barnes Notes

Quoted verses:
Romans 12:17
Recompense to no man evil for evil. Provide things honest in the sight of all men.

Here is the commentary on this verse:
 

 Here is the commentary on 2 Corinthians 8:21

2] And specially for those of his own house.

Those of his own house - That is, his own family, or a poor widow or relative that lives under his roof. ~Adam Clarke

And specially for those of his own house - Margin, “kindred.” The word “house,” or “household,” better expresses the sense than the word “kindred.” The meaning is, those who live in his own family. They would naturally have higher claims on him than those who did not. They would commonly be his nearer relatives, and the fact, from whatever cause, that they constituted his own family, would lay the foundation for a strong claim upon him. He who neglected his own immediate family would be more guilty than he who neglected a more remote relative. ~Barnes Notes

And specially for those of his own house - that is, who are of the same household of faith with him; see Galatians 6:10, and so the Syriac version renders it, "and especially those who are the children of the house of faith"; for though the tie of nature obliges him to take care of them, yet that of grace makes the obligation still more strong and binding; and he must act both the inhuman and the unchristian part, that does not take care of his pious parents: wherefore it follows, ~John Gill

Quoted verse:
Galatians 6:10
As we have therefore opportunity, let us do good unto all men, especially unto them who are of the household of faith.

3] He hath denied the faith.

Hath denied the faith - The Christian religion, which strongly inculcates [teaches frequently] love and benevolence to all mankind. ~Adam Clarke

he hath denied the faith - the doctrine of faith, though not in words, yet in works; and is to be considered in the same light, and to be dealt with as an apostate from the Christian religion. ~John Gill

He hath denied the faith - By his conduct, perhaps, not openly. He may be still a professor of religion and do this; but he will show that he is imbued with none of the spirit of religion, and is a stranger to its real nature. The meaning is, that he would, by such an act, have practically renounced Christianity, since it enjoins this duty on all. We may hence learn that it is possible to deny the faith by conduct as well as by words; and that a neglect of doing our duty is as real a denial of Christianity as it would be openly to renounce it. Peter denied his Lord in one way, and thousands do the same thing in another. He did it in words; they by neglecting their duty to their families, or their duty in their closets, or their duty in attempting to send salvation to their fellow-men [spreading the gospel], or by an openly irreligious life. A neglect of any duty is so far a denial of the faith. ~Barnes Notes

4] And is worse than an infidel.

Is worse than an infidel - For what are called the dictates of nature lead men to feel for and provide for their own families. Heathen writers are full of maxims of this kind; Tacitus says: Liberos cuique ac propinquos Natura carissimos esse voluit. “Nature dictates that to every one his own children and relatives should be most dear.” And Cicero, in Epist. ad Caption: Suos quisque debet tueri. “Every man should take care of his own family.” ~Adam Clarke

And is worse than an infidel - for the very Heathens are taught and directed by the light of nature to take care of their poor and aged parents. ~John Gill

And is worse than an infidel - The word here does not mean an infidel, technically so called, or one who openly professes to disbelieve Christianity, but anyone who does not believe; that is, anyone who is not a sincere Christian. The word, therefore, would include the pagan, and it is to them, doubtless, that the apostle particularly refers. They acknowledged the obligation to provide for their relatives. This was one of the great laws of nature written on their hearts, and a law which they felt bound to obey. Few things were inculcated more constantly by pagan moralists than this duty. Gelgacus, in Tacitus, says, “Nature dictates that to every one, his own children and relatives should be most dear.” Cicero says, “Every man should take care of his own family “ The doctrine here is:

(1) that a Christian ought not to be inferior to an unbeliever in respect to any virtue;
(2) that in all that constitutes true virtue he ought to surpass him;
(3) that the duties which are taught by nature ought to be regarded as the more sacred and obligatory from the fact that God has given us a better religion; and,
(4) that a Christian ought never to give occasion to an enemy of the gospel to point to a man of the world and say, “there is one who surpasses you in any virtue.” ~Barnes Notes

I want end with a couple of quotes regarding care for the family.

"Too often we underestimate the power of a touch, a smile, a kind word, a listening ear, an honest compliment, or the smallest act of caring, all of which have the potential to turn a life around."

"Never believe that a few caring people can't change the world. For, indeed, that's all who ever have."

"My guiding principles in life are to be honest, genuine, thoughtful and caring." ~Prince William

"Live so that when your children think of fairness, caring, and integrity, they think of you."