From what I've read, even being vaccinated for diseases like Polio, it is possible to contract it and spread it. It's when there is herd immunity through vaccination, that even when it is contracted or passed, the immune system knows about it and protects against paralysis. Vaccinated individuals contracting polio leads to no symptoms (or mild gastro symptoms), but the ability to spread to unvaccinated individuals.
I'm not condemning you nor commending you on not getting vaccinated. I'm only pointing out that vaccines don't create a forcefield around you that keep you from contracting or spreading disease. They increase the likelihood of herd immunity by making the immune system aware and therefore reduce spread and reduce the likelihood of the worst outcomes.
I personally don't remember messaging that said if you get the Covid Vaccine that you can't get or spread it, but instead that it would reduce symptoms and spread while increasing herd immunity. I remember specifically hearing that if herd immunity was not achieved, that the vaccines would be far less effective in reducing spread, but that those vaccinated would be more protected against the worst effects.