"Go climb a tree" is like several other American expressions or idioms:
Go jump in the lake. Take a flying leap. Take a long walk off a short
pier. Go fly a kite. Go chase yourself. And here's a really old one --
Go to grass and eat hay.
They all mean "go away, leave me alone."
It means "go away and stop bothering me." The person doesn't want someone to actually climb a tree.

I really love it)))

I mean I am going to love American LOL English