Why does Hellboy file his horns?

Hellboy most likely files his horns in order to fit into human society. Despite his fearsome appearance as a red skinned half-demon, Hellboy has a good heart and desires to love and get along with humans. Humans find the presence of demon horns to be off-putting. Filing them so that humans will feel comfortable around him makes sense. Despite Hellboy’s infernal origins, when he was summoned in 1944 from Hell, he was just a baby and was raised as a human boy by Dr. Trevor Bruttonhelm.

Since he was raised as a human, he probably has a desire to be more human prompting him to file his horns to assume a somewhat more human appearance. Despite his filed horns, when he is under stress, Hellboy can go through a transformation in which his horn stubs grow into full horns and he gains bat-like wings. For the sake of humans that he is working with though, he probably tries to minimize his more infernal attributes.