You can be fully vaxed and catch covid. You can also be fully vaxed and still spread it. Being vaxed can only "possibly" help the individual that has been vaxed. It does not lessen the possibility of spreading the virus.
Do you not know that the vaccinated are getting infected and also spreading the virus? My guess is that since there are more vaccinated than not, they are doing the most spreading. How else is it spreading so fast?