You are right that the learning process which ANNs use is pretty much nothing like the brain. But an argument can be made that the feature representations which they learn are quite brain like. For example in visual cortex, you will find feature detectors for things like edges and whatnot, with more abstract features as you climb to higher layers. You see very similar things in Convolutional nets.

Spiking neural network models are actually very brain like, but no one really knows how to use them effectively.

I think its also important to realize that we don't have simulate the brain to do what the brain does. If you want to build a flying machine, you could model a bird with flapping wings, but its much easier to just build a fixed wing aircraft. Back propagation may be a similar case. Evolution found a very good way to learn with neurons but it may not be optimal for the things we care about. We may be better off sticking to back propagation because it works so well. Also people are investigating backpropagation alternatives which start to look more and more brain like.

Basically my point is there seems to be intrinsic characteristics of neural computation, which ANNs and real brains both demonstrate.