Objection 1. It seems that piety does not provide support for our parents. For, seemingly, the precept of the decalogue, "Honor thy father and mother," belongs to piety. But this prescribes only the giving of honor. Therefore it does not belong to piety to provide support for one's parents.
Objection 2. Further, a man is bound to lay up for those whom he is bound to support. Now according to the Apostle (2 Corinthians 12:14), "neither ought the children to lay up for the parents." Therefore piety does not oblige them to support their parents.
Objection 3. Further, piety extends not only to one's parents, but also to other kinsmen and to one's fellow-citizens, as stated above (Article 1). But one is not bound to support all one's kindred and fellow-citizens. Therefore neither is one bound to support one's parents.
On the contrary, our Lord (Matthew 15:3-6) reproved the Pharisees for hindering children from supporting their parents.
I answer that, We owe something to our parents in two ways: that is to say, both essentially, and accidentally. We owe them essentially that which is due to a father as such: and since he is his son's superior through being the principle of his being, the latter owes him reverence and service. Accidentally, that is due to a father, which it befits him to receive in respect of something accidental to him, for instance, if he be ill, it is fitting that his children should visit him and see to his cure; if he be poor, it is fitting that they should support him; and so on in like instance, all of which come under the head of service due. Hence Tully says (De Invent. Rhet. ii) that "piety gives both duty and homage": "duty" referring to service, and "homage" to reverence or honor, because, as Augustine says (De Civ. Dei x), "we are said to give homage to those whose memory or presence we honor."
Reply to Objection 1. According to our Lord's interpretation (Matthew 15:3-6) the honor due to our parents includes whatever support we owe them; and the reason for this is that support is given to one's father because it is due to him as to one greater.
Reply to Objection 2. Since a father stands in the relation of principle, and his son in the relation of that which is from a principle, it is essentially fitting for a father to support his son: and consequently he is bound to support him not only for a time, but for all his life, and this is to lay by. On the other hand, for the son to bestow something on his father is accidental, arising from some momentary necessity, wherein he is bound to support him, but not to lay by as for a long time beforehand, because naturally parents are not the successors of their children, but children of their parents.
Reply to Objection 3. As Tully says (De Invent. Rhet. ii), "we offer homage and duty to all our kindred and to the well-wishers of our country"; not, however, equally to all, but chiefly to our parents, and to others according to our means and their personal claims.
Source: Summa Theologica (New Advent)