I did check the mesh for rough edges. It had a few spots, so I retrimmed the whole thing and cut down the middle of the solid rows so that there was no risk of having any sharp edges from the horizontal rows that were previously cut. It's all soft now, and he swam around it long before his fins started ripping. But I retrimmed it and the one's belonging to the other males just in case. I have wondered about the plastic plant, but again he had it long before the fins ripped. I will be taking it out though and replanting with silk plants from the craft store.
It could be any of these things really I guess, but I wanted to make sure no one thought it was him biting them. The missing chunk of his tail looks like he bit it, but the rips on the other fins do not to me.