Your mom and dad can live together and one can get COVID but not the other because of everyone's immune system being different. Vaccine or not. Your immune system is different from another person's.
Let me put it in a way you can understand, if you and your friend both BBFS the same girl, he gets herpes but you don't. Same exposure, different immune systems. There is no logic or reason for this, at lease none that scientists have offered us. So we are required to adopt "blanket" approaches like vaccination that "may" work for everyone.
You are right, it doesn't work the same for everyone, just like not everyone gets infected by the same virus subjected to the same exposure.
The thing is, vaccine is like insurance, it is better to have it and not need it; rather than need it and not have it. If you are a total anti vaxxer then that is your right too, but then stay the fuck home so other people don't get exposed to your virus load sprayed with each breath. That is the common courtesy decent thing to do, and wear a mask when you are in public places too.