[Wyoming23]

You're confusing "teaching assistants" with teaching a class.

A typical setup would be to have a professor give 3 lectures a week, along with open office hours, and design the curriculum. Then to have an assistant or two who are graduate students (people who have a bachelor's degree or master's degree in the subject) who help grade homework, set up lab work, and answer student questions in a 1-hour recitation/discussion meeting.

[sgc]

That's not the case in many places (including prestigious universities - and due to their research orientation, perhaps it happens more, the more prestigious it is).

It is virtually impossible to get into a teaching position post-doctorate in the US if you have not been teaching as a doctoral candidate. I have taught in Unis where there was an entire team of doctoral candidates (and a couple master's candidates) teaching a big chunk of the classes offered to undergrads - not as assistants, just as the listed "professor".

I have also followed open courses online where the "Prof" gives two or three classes in the semester, and the "assistant" teaches the rest.

As far as I know and have experienced, what you are describing is less true every year.