I've been teaching programming for eight years now, and I'd say "What we do isn't that hard." If we were writing 3D game engines, yes we'd need insane levels of math, theory, etc.
But writing web applications is mostly about following smart patterns, getting something done, done quickly, then improving the hotspots that need it. I can teach you to do that in five months, no problem.
Then it just takes a lifetime of practice to be, truly, good.
j3 is right -- developing web apps, 95% of the time, is a trade and not something that requires a four year CS degree. I've taken several people from scratch and taught them enough to be useful to me over a 4-5 month period; years later some of them are holding down very highly paid web development jobs.
But writing web applications is mostly about following smart patterns, getting something done, done quickly, then improving the hotspots that need it. I can teach you to do that in five months, no problem.
Then it just takes a lifetime of practice to be, truly, good.