Magnetic induction would also apply opposing forces to the launch satellite, but that doesn't matter if the launch satellite is just as disposable as the slugs that destroy the target.
Inert gases are too heavy, only if the weapons program tries to collect them on the ground and launch them into orbit.
I'm obviously making things up, because this is a system open to invention, given that it doesn't actually exist yet. This concept is less practical, if you operate within existing constraints, using only rocket propellant to boost objects into orbit, and then subsequently de-orbit them.
Game changers emerge, when new ways of operating in space appear. Even if this is "less practical" right now, after the introduction of adjacent technologies, as an existing concept it could suddenly become practical. For example, with the introduction of a space elevator, boosting such a weapons system into orbit is less costly. Then, more of its components become readily disposal at practical values.
I'm not required to operate within existing economic constraints, to consider ideas that are not actually limited by physical laws.
Propellant is a conventional means, but certainly not the sole means. Magnetic induction could eject a slug from an orbiting platform, or inert gases could jettison to induce motion. Burnt fuel isn't a requirement.
You insist on a rocket motor. But you just resist the idea of this form of orbital weaponry.
A large enough asteroid could enter into earth's gravity well and chart a straight line to impact.
You presume preconceived concept of a weapons platform already in orbit, controlled from the ground, or by a terrestrial entity. But a weapon of lunar origin might insert into the atmosphere differently. As with any weapon, an approach to target should be the least defensible path. After atmospheric re-entry, when position is given away, you'd want the penetrator to travel as perpendicularly to the target as possible, but prior to that moment, any stealthy approach is game.
I'm not 100% wrong. You're 100% obstinate.