Analogy of someone throwing an object is wrong. People that say “conservation of momentum bruh” don’t know what they are applying it to.

“ Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system. It is embodied in Newton's first law (the law of inertia).”

The external force is provided by pressure gradient force (yes it is a force that can be calculated), not the rocket.

Since rockets do not push the exhaust out, there can be no opposite force on the rocket. Rockets work in atmosphere because the exhaust pushes on the atmospheric pressure. There is no atmosphere in space for the rocket to push off of. Hence every rocket launch, the rocket ends of moving horizontally and not straight up. Orbit is simply an excuse for dishonesty