And it appears that someone has used a liberal amount of silicone caulk during its installation or to "repair" a leak. That drain cup may be full of silicone caulk which can be very difficult to remove.
As havasu just said, I would use a Dremel tool and cut the drain cup down one side and try to pry it off. If that wasn't successful, cut the other side and you should be able to finally pry it off. Use a utility knife, razor blade scraper, and/or Exacto knife to cut off the silicone caulk and you should be able to remove that drain.
I had one in a house I owned, while replacing the kitchen sink, found that they had GLUED the top strainer, onto the top of the sink...... I guess they wanted to make SURE they had ZERO leaks.... it was some kind of epoxy, I guess, VERY hard....