Anchor won’t penetrate wall?
My guess is that you are hitting concrete behind the drywall or you luckily selected a spot with plumbing, electrical or something else running behind it.  It could even be wood behind it, which would be good, as you could screw directly into the wood, but you need to confirm that.  

I would take the drywall anchor out and tap in the hole it made to see if it sound like a hard or wood surface.