A rocket works this way

a mass little m is ejected in this direction => at velocity big V
the rocket's mass big M moves in this direction <= at velocity little v

mV=Mv

the ejected mass m is a fraction of the rocket's mass M but its velocity V is very high making the product mV large enough to move the big fat rocket's M

you have the rocket move in the oposite direction of the ejected mass
equal and opposite reaction, given mass times velocity

NOTHING pushes against anything
there is no push against

In real rockets most of its mass M is fuel which is ejected at wicked high V a little m fuel at a time. The bigger V is, the higher the rocket's specific impulse (ISP) is or its fuel efficiency