Hebrew poetry (such as Psalms and Proverbs) are noted not for rhyming but for parallelism. That is, they will often make a statement in the A part of the verse that is repeated slightly differently in the B portion. Proverbs 15:20 is a good example of using contrast in the parallel.
A wise child(A) brings joy(B) to his father(C),
but a foolish person(A) despises(B) his mother(C).
This verse is almost identical to Proverbs 10:1
A wise child(A) makes a father(C) rejoice(B),
but a foolish child(A) is a grief(B) to his mother(C).
In this one, the parallels are marked according to the Hebrew word order which has "makes rejoice" in one word before father.
You can take any verse of poetry and find these parallels. They might be showing a contrast (as here) or repeating for emphasis as in Psalm 1:1:
1:1 How blessed is the man who does not walk in the counsel of the wicked,
Nor stand in the path of sinners,
Nor sit in the seat of scoffers!
The NASB shows the structure much better than the NET here. The verse is formatted to show the structure. One should not base a teaching on any kind of distinction between the counsel of the wicked, the path of sinners, or the seat of scoffers.
The writer of the proverb was not trying to say that wise men come from the father while fools come from the mother. He was making a contrast.