Why does Hellboy file his horns off?

Are you talking about the graphic novel or the movie by Guillermo del toro? Del Toro summed it up though.... Hellboy files his horns down (they're still there, just small stumps) to try and fit in and appear more human. It's apparent he has self-image issues considering he works with all humans and fights monsters.

His right hand is a stone that IS his natural hand that science could not identify or explain. It opened the gate Rasputin tried to open to bring down the 7 lords of chaos from space.

(Grigori Efomivoch Rasputin was a real historical figure who brought bad reputation to the last czar's family)

He files his horns to stumps because he believes it makes him look a little more human than normal. Really its just a self confidence thing.

And his hand is actually a stone that medicianal science cannot identify. His hand it the key to a alternate dimenison. The bad guy tried to open it to let loose a fallen deite on the earth trying to turn it into a living hell.

He files his horns down in an attempt to be somewhat normal........if that's at all possible, I think in the first movie he's still a little self conscious about his appearance

I am probably wrong, and I only saw the movie once, but I think its because he is against being sent to Hell. its like a rebellion type thing.