Comment by unwind
Uh, is it really clear to say that rockets "push against" something? That makes it sound as if they could absolutely not work in space, which they obviously do.
"They push against their own exhaust" seems to be the idea that motivates the pushing explanation, but to me that just invites the question "using what?" and makes things even more complicated. At least in my opinion.
I think Newton's 3rd ([1], forces and reaction forces) is a better explanation.
[1]: https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion
> rockets need something to push against, they have to carry it with them.
(Emphasis added)
The rocket exhaust is "pushing against" the rocket itself, propelling it forward.
Rocket exhaust goes <- which creates the equal and opposite force -> which pushes against the mass of the rocket sending it on its way.