Why did I need to switch several appliances in order to power my electric stove?
I'm assuming you are in the United States for this answer. A stove is normally on a dedicated circuit which means it alone is the only load wired to a particular circuit breaker. This means nothing else would have been affected if your stove's breaker tripped. The breaker for your stove will be larger than a normal 120V breaker in your panel so you would have had to reset this if the breaker indeed tripped. If your stove was still on, resetting the breaker may have been difficult; the switch may have been difficult or impossible to switch to the "ON" position.

I am assuming you unknowingly reset the breaker when you were switching things in your breaker panel. If you are certain you didn't, then you may have never actually tripped a breaker and have some other electrical problem.