Equal and opposite reaction.
There's a law for this. The matter is "pushing" against the ship, it doesn't have to push against anything else.
In fact having an atmosphere to push against actually reduces the effectiveness of thrust due to atmospheric pressure, which must be overcome. Which is why different engines are designed to run in atmosphere versus out of atmosphere.
If you throw a baseball in space you have transferred momentum to that baseball, pushing you back. You will move in the opposite direction (likely spin because you just imparted angular momentum onto yourself since you didn't throw from center of mass)
Am I saying you are scientifically illiterate?
Based on the previous statements, yes. However, as a matter of fact, not necessarily insult.
The good news is you're following up with questions and want to learn more, instead of doubling down. With curiosity you will become more literate.
The education system in the country you are from has failed you. Assuming you are in your mid-late teens, or older, scientific topics should have already been taught in what North America would call "middle school" (11-14 years old). That teaches you things like conservation of momentum.
There is a reason why it's called illiteracy, because there is an expectation that the baseline level of education everyone in developed countries receives teaches them the fundamentals of how the world around them works. Without this fundamental understanding it's not possible to understand more complex topics that build upon it, stunting growth.