I imagine that the problem isn't really that he wants A girlfriend. Anyone could get a completely random chick for a girlfriend, but that relationship would be pretty meaningless.
I can only assume that the aforementioned INTP wants to be understood and not be criticized by someone else. He wants someone to appreciate him for who he is. Of course many people can fit this role; however, I find it extremely difficult to reciprocate such a state of mind without there being some sort of "click," "spark," or instant connection.