Didn't he make them after hours in a chemsitry class? I didn't read a lot of the early spidey comics, but seems like they portrayed him in the lab quite a bit. I think he even helped Doc Connor with his research going after class to be his lab assistant. He's often utilized as a science/tech guru in the comics, so I do like the artifical web shooter concept for the fit with the books. That said, if he has all the other powers of a spider, it would make sense that he can shoot webs too.