How come capacitors can "see" if they don't have eyes?

Finding I have no potential
I can't find the differential!
Oh it sucks and now I'm worried
Studying's becoming hurried.
Brain is putting up resistance
Even through my mad insistence
Just can't seem to learn this stuff
Now the going's slow and rough.
None of this makes sense to me
Any kind of fool can see:
Every op amp, each transistor
Gives me one more mental blister.

So, I'd like to take some time and spill some random stuff about Circuits, and why this course makes me mad.

Firstly, why are there so many assumptions? I remember being told all the while growing up that making assumptions was a very bad thing. I remember. My mom used to yell at me all the time because I'd assume things about stuff, whether it was first impressions of people, or judging a book by its cover, or assuming that something would just get done without my doing it. Yelled at, all the time. "Assuming makes an ass out of u and me," she used to say. It was like once a day. Even my grade 3 teacher, Mrs. Risavy used to say it all the time. Then in high school, my calculus/algebra & geometry teacher. Same thing.

Assumptions are bad. Assumptions are bad. Assumptions are bad.

Now...we're making assumptions all over the place! And suddenly, it's okay! Assumptions -- and I have no idea where they're coming from. So random. For example: looking into the drain of this MOSFET, we can see (obviously) that the look-in resistance is Ro. And then looking into the source of this one (clearly) you can see that the output sees a resistance of 1/gm. So obvious. And (of course) we can just neglect this here and that there, and because it's so obvious that the input resistance has no effect on the node, and since I decided to do a handstand before attempting this the transconductance can be neglected in the drain. Oh wait, I almost forgot. I'm wearing green today. That means that you have to include the body effect in the third FET.

Confused...I don't get it. Why can I make these assumptions and why is it that Circuits only makes an ass of me?