Why is 13. Bh3 so bad here?

Just watching a Ben Finegold lecture on this game:

You can see his reaction at 3:11.

I don't understand why it's that bad. Is it better to just leave the bishop on g4 and trade with the knight?

Yeah, but why is the bishop on h3 that bad? It is on a pretty long diagonal... it's attacking that pawn. It's protected by a pawn. I don't understand why it's that bad. What would be an ideal square for the bishop?

Very good question. Perfectly normal move for a simple mind like me. Also, it is the top engine move. I did not watch the video. Didn't he elaborate?

Well he didn't like 12. Bg4 either. So maybe he thought the bishop should have remained on e2. I can kind of see that as the bishop on e2 can go to both kingside and queenside. He didn't really explain why he didn't like it. He just shook his head like it was the worst square for the bishop.

Ok, so he didn't like the whole Be2-g4-h3 thing. That makes more sense. I guess one wants that Bishop maybe on d3 and go for a kingside attack.

There is nothing wrong with 13 Bh3. However 12 Bg4? is a mistake. 10 Nd4? is also a mistake. 

Why is Bg4 a mistake?

#8
12 Bg4? and 13 Bh3 does not work. 13 Na4 was fine for white.
10 Na4 was even stronger: hang on to the extra pawn.