What Quagmire said.
The Engineer is basically a knob-twiddler and operates the desk and adds the FX like reverb etc. Plus technical stuff like compression.
Well no, there's a huge amount more in engineering than that. You need to get microphone placement correct amongst other things, and that takes a bloody age usually. There's a lot of twanging whatever, deciding that it needs more of something or other, moving the microphone and re-iterating the entire process. Yes, the engineer is also the one who works the knobs, but there's a ton more to it than just that.
Mixing is also where a lot of tweaking with putting effects such as reverb, filters and EQ in, not just getting the levels right. Even if the levels are "right", you can still have one thing trampling over everything or being trampled over if you don't apply the correct stuff to it in the mixing stage. Mixing takes a hell of a lot of practice to get right, and has the potential to be horribly influenced by what room or kit the mixer uses.
It's especially un-simple in prog, where different sections of a single song have the potential to require vastly different mixes. I remember around the time Spock's Beard released X, one of the Beard guys saying that getting everything to change the right amount at the right rate between sections of longer songs meant that mixing a thirty second transition took roughly the same amount of time as an entire five minute song of a more straightforward nature.
The technical side of music is just as, if not even more complex and difficult than the writing and playing it.