Why would a monkey give birth to a human?

You are confusing tree branches (1-monkeys, 2-humans) with tree trunks (DNA). Looking at a tree, you'll notice that the branches are never the same and yet they all come from the same trunk. Branches can fork, split, or twig, but branches don't beget other branches, trunks do. The connection between monkeys and humans is through the tree trunk, the ancestral DNA.

First of all it's apes we are closely related to not monkeys. That's a different branch.

Secondly, we are not said to have evolved "from" apes. We share a common ancestor with modern apes. That ancestor may superficially look more like othet modern apes than a modern human but only the DNA tells the true story of which is more like which and the import of that is even debatable. Even taking that resemblance for granted, there is no reason it had to be such. After speciation divided us from our last obviously ape ancestor, it was altogether likely one of us would diverge faster. It happened to be us.