This proverb suggests two things about a wise son. First, he became wise from responding appropriately to his father’s discipline (“instruction”). Second, a son who is already wise will continue to pay attention to his father’s instruction.
Wisdom is not magical, it is totally accessible to anyone who is open to receive it. One of the major sources of wisdom in most of our lives is going to be parents or the other loving caring adults in our lives who offered instruction/discipline to us.
The second half of the verse reminds us that a mocker/scoffer/cynic does not receive rebuke very well from anyone. This is a person who rejects moral principles, spiritual insights and personal accountability.
The different response from these two people is very simple – one accpts instructions from others, the other doesn’t. That single lifestyle choice makes them remarkably different people.