^^Umm... ick. Somehow I don't think comics readers in the 1960s would've been too comfortable with the idea of a superhero leaving his own bodily secretions dangling off of buildings all over the city. Heck, I'm not too comfortable with that.
The comics' explanation is that Peter isn't just a clever tinkerer, he's a genius. He has a gift for scientific invention.
Then, like Reed Richards and Tony Stark, they should show him actually inventing things.
The character they show on a regular basis doesn't have that capability.
Like I said, it doesn't have to be in his arse. The organic web shooters in his forearms shown in the movie are bodily secretions BTW. There's just no capacity in nature to "shoot" webs that distance, or the relative distance for something a spider's size. So I can see him loading up a mechanical spray device with his own web fluid, but not his body spraying it more than a few inches.
Anyway, I'll go back to suspending my disbelief.