This is a poem from a book of poetry for children.
The basic message to the child is all the negatives the child will hear are wrong. The author is really suggesting not listening to them; the truth is that “anything can happen, anything can be.”
So the author is not suggesting that the child attend to weaknesses-just the opposite.
Poetry cannot be expected to parse as standard English.
You could think of “don’t“never haves” as, for example, “You don’t“You'll never have any chance of going to college.”
See the Wikipedia page for the author.