[duped]

Ultimately an op amp is a hardware abstraction. Often you teach the abstraction first through its interface to understand how it allows building useful things. Then you can teach the implementation behind that interface, and all the design trade offs. And just like the formulae, you need to understand that it's a tool for simplification - distrust shouldn't come into play, just proper understanding.

At least in my EE undergrad we were taught why you would want an op amp before we were taught how to design multi stage amplifiers with discrete transistors. In fact most of the real world limitations of op amps don't require knowledge of what's going on under the hood, least of all the physical layout of the chip. Even a schematic diagram of the simplified model for a UA741 is more than you'd ever need except for a shitty SPICE emulation.

I empathize with what you're getting at, but I've seen that mentality turn into the bane of practical or working knowledge of many technical topics. It is a skill to be able to learn just what you need to learn and decide what level of detail is enough, and most of the time that skill is only provided through instruction and mentorship.