"On My First Son" isn't just about the speaker's son, it's also about the powerful feelings of love and affection he feels toward his child. These strong feelings make the child's death, especially at such a young age, incredibly tragic and painful for the speaker. The speaker suggests that having feelings that are too strong ultimately makes his loss that much worse. By the poem's end, he decides to avoid having feelings that are too intense for the things he loves. He ends up like the opposite of this guy.
The speaker's concluding vow suggests that he will never really "like" anything seriously ever again. He wishes to kill his ability to have strong feelings. Bummer.
Puh-lease. The speaker is fooling himself. There is no way to love something and not "like" it too much.