(This is more of a “medical-psychological answer” than a “celebrity answer”).
Because he suffers from very severe prosopagnosia (face blindness).
There are quite a few gradations of it. I have it myself, but it's not so severe that it becomes a disability.
But when I watch a movie in which there are several people dressed similarly, I usually can't tell them apart. I need clear clues. For example, a birthmark or glasses.
In the case of Brad Pitt, it is said to be very pronounced.
He himself has said that a lot of people hate him because he simply doesn't recognize them. They think he's arrogant and that he doesn't want to talk to them.
It's also extremely uncomfortable when someone comes up to you and greets you as if you know each other well and you can't place them.
It happens to all of us sometimes, and it's unpleasant.
But it just doesn't happen all the time.
It is said that Brad Pitt does not recognize his sister's children.
And that he had constant stress with Angelina Jolie because she called him arrogant.
After all, you may not realize you have face blindness until adulthood.
To give you an idea of what it's like:
When you look at face sequence A, if you can distinguish "normal" faces, you can see four different faces. Quite easily, in fact.
I don't see the difference at first glance, by the way. I have to look at the details for a very long time to see the difference.
And for those who are face blind, the faces look the same as in sequence B.
So it is not so easy to be at a party .
In extreme cases, those affected cannot recognize their own partners. And some don't even recognize their own face in the mirror. They have to feel their face.
One in 40 is said to suffer from face blindness.
Among them is Crown Princess Victoria of Sweden or author Oliver Sacks.
The best strategy to cope with it is to be open about it, at least I think so.
Don't cover up the fact that we don't know who the other person is.
And make your own face blindness public.
Brad Pitt has taken this step. But he still prefers to be with people he knows very well.
And, offtopic: He doesn't do anything to his face apparently and just gets older. Nice.
Disclaimer:
English ist not my mother tongue, pardon my mistakes.
Please do not translate my answers, because i do it by myself.