Why is Bxa8 a mistake?

You might have left something hanging, and the opponent didn't notice

Posted, do you see it?

After black recaptures on a8 white will have difficulties along the diagonal which ends up

giving white too much trouble for a mere exchange.

you've just posted an image, but maybe it's becuase your opponent gets a big attack and development in the return for the rook, although your opponent would need to be pretty good to not lose. (I need stockfish to back me up becuase Ireally am just guessing.)

I'm going to guess that this was the game with 6...N8d7 played instead of 6...Be6. After playing through some lines with Stockfish on this site, the best explanation I can give is that black gains the center and a development advantage as compensation for the exchange. The position for black does feel like it would be easier to play the exchange down. That might be why there is a 1 point swing in favor of black (Going from a +.5ish evaluation for white to a -.5 evaluation in favor of black).

I'm hopeful that a better player than myself can provide a better explanation than what I provided.

The original position is difficult. Basically the b7 bishop is stronger than the a8 rook, that's why it's a mistake to "win" that exchange. The bishop is the king of the long diagonal, while the rook is just sitting there in the corner doing nothing.

I am on GM-Level or WC-Level but I can not see why this should be a mistake.

That was a nice way to mate black, wasn't it just?