Why would Catholics believe that being kind to one's father will bring reparation for sins?

Consider this passage from the Gospel of Matthew, chapter 25 (as usual, emphasis is mine):

34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:

35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:

36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.

40 And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done [it] unto one of the least of these my brethren, ye have done [it] unto me.

41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:

42 For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink:

43 I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not.

45 Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did [it] not to one of the least of these, ye did [it] not to me.

46 And these shall go away into everlasting punishment: but the righteous into life eternal.

Now, to someone who does not quite get the perspicuity of Scripture, this passage might be construed as arguing that the righteous are justified because (for, v. 35) they fed, gave drink, shelter, clothing, or visited "the least of these my brethren" (v. 40). And the others are condemned because (for, v. 42) they did not feed, give drink, shelter, clothing or visit "one of the least of these" (v. 45).

Now, Protestants clearly do not hold that this Gospel "goes against everything in Scripture". I believe the explanation is that those who do the Corporal Works of Mercy described in the Gospel are simply showing visible signs of their internal conversion, operated by faith — any Protestant brother, please correct me in the comments if that impression is mistaken.

By the same token, the passage in Ecclesiasticus (AKA Wisdom of Sirach) 3:14, when it says (re-quoting the KJV for consistency with the Gospel I quoted above):

14 For the relieving of thy father shall not be forgotten: and instead of sins it shall be added to build thee up.

Here the Sacred Writer enjoins his readers to be kind to their parents because the kindness shown to the parents is also a Corporal Work of Mercy, which Jesus (this time the Son of God, not of Sirach) mentioned in his sermon in the Gospel, and "every tree is known by his own fruit; for of thorns men do not gather figs, nor of a bramble bush gather they grapes" (Lk 6:44). And a man who cannot respect his own father and mother will certainly not respect a complete stranger, nor the Father who is in heaven.

Furthermore, the Catechism says of the duties of children, in the section commenting on the Fourth Commandment (honour father and mother):

2215 Respect for parents (filial piety) derives from gratitude toward those who, by the gift of life, their love and their work, have brought their children into the world and enabled them to grow in stature, wisdom, and grace. "With all your heart honor your father, and do not forget the birth pangs of your mother. Remember that through your parents you were born; what can you give back to them that equals their gift to you?"^{Sir 7:27–28}

2216 Filial respect is shown by true docility and obedience. "My son, keep your father's commandment, and forsake not your mother's teaching.... When you walk, they will lead you; when you lie down, they will watch over you; and when you awake, they will talk with you."^{Prov 6:20–22} "A wise son hears his father's instruction, but a scoffer does not listen to rebuke."^{Prov 13:1}

2218 The fourth commandment reminds grown children of their responsibilities toward their parents. As much as they can, they must give them material and moral support in old age and in times of illness, loneliness, or distress. Jesus recalls this duty of gratitude.^{Cf. Mk 7:10–12}

For the Lord honored the father above the children, and he confirmed the right of the mother over her sons. Whoever honors his father atones for sins, and whoever glorifies his mother is like one who lays up treasure. Whoever honors his father will be gladdened by his own children, and when he prays he will be heard. Whoever glorifies his father will have long life, and whoever obeys the Lord will refresh his mother.^{Sir 3:2–6}

O son, help your father in his old age, and do not grieve him as long as he lives; even if he is lacking in understanding, show forbearance; in all your strength do not despise him.... Whoever forsakes his father is like a blasphemer, and whoever angers his mother is cursed by the Lord.^{Sir 3:12–13.16}

2220 For Christians a special gratitude is due to those from whom they have received the gift of faith, the grace of Baptism, and life in the Church. These may include parents, grandparents, other members of the family, pastors, catechists, and other teachers or friends. "I am reminded of your sincere faith, a faith that dwelt first in your grandmother Lois and your mother Eunice and now, I am sure, dwells in you."^{2 Tim 1:15}

In conclusion, Catholics dispute that the passage in Ecclesiasticus/Sirach 3 is "against everything in Scripture", because there is plenty in Scripture (not just the Deuterocanonical books) where "justification by works" can be read into the text, like the Gospel passage first mentioned in this answer.