Origin of human intelligence and thought
How is 


"we don't descend from any Chimpanzee or Orangutan because, if we did, they would also have the cognitive thinking ability that we have"


not equivalent to


"We are not related to the chimpanzee or orangutan because, if we did, they would also have [the same amount of body hair]/[the same sized mouths]/[the same muscular strength] that we have"


?

Any related species are going to differ in some respects (otherwise they would not be different species, after all), and it is plain to see that intelligence is one of the ways in which species can differ.

Regardless of that (if your friend thinks intelligence is special in a way that hairiness is not), you can make your argument even while sticking to talking about intelligence, and there is no need to go into the reasons for changes (increases) in intelligence to see that.

To make the point with your friend, it might be best to point to two different animals that


she recognizes as related, and that
she also recognizes as having different levels of "cognitive thinking ability".


In light of such an example, her argument falls flat (unless she further considers only human thinking ability special, in which case you will have a harder time!)