Help with a position

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rafa1906

Hello,

I am relatively new to using chess.com (frequently, at least), so I don't know if I should post this here, but from what I've seen this seems to best place.

Recently I was playing a training game and I reached these two positions:

 
 
 
In the first I played Ba4 and in the second I played to Rd1 (to increase pressure on d4 though in retrospect it probably wasn't the best idea).
 
 
The problem, however, is that in both positions the engine suggests Bxc6 and I can't understand why. During the game I avoided capturing the knight because:
 
 
a. The knight on c6 is pinned so I figured it was a bad piece since at least as of yet it's not a relevant defender of d4/ attacker of e5
 
b. I would be giving up my bishop pair which I figured was important to keep since he has a bad light-squared bishop
 
c. If Bxc6 bxc6 he would get a semi-open b file for his rook on a8.
 
 
So what did I overlook and why should I play Bxc6?
rafa1906

And if someone asks, yes, I learned afterwards that Bb5+ is a bad move in the Advance French, but as you can guess I am still a bit of a noob and didn't know it at the time xD