Feels like the movement for both characters needs a lot more polish and fluidity (and "don't hold space or you won't climb the ledge" needs to be explained imo), and maybe the spider will be fun to play as then.
Honestly I don't think it's doing anything new, but if you fine-tune the spider and come up with more mechanics for it, it might turn out to be a fun platformer. I really like how the spider flops its legs around, which already makes it more fun to play.