He got 4 shots and still got it. I don't think you need to be an "anti-vaxxer" to know they don't prevent transmission.
Not only would you need to be an anti-vaxer but you would also need to redefine the word prevent.
Prevent means to reduce the probability of something happening not make it impossible.
For example:
Condoms prevent the transmission of STDs.
Helmets prevent brain injuries.
Warm clothing prevents hypothermia.
Drinking water will prevent heat stroke.
Seat belts and air bags prevent auto fatalities.
Wearing sunscreen prevents sun cancer.
etc, etc, etc.
The vaccine does three things:
1. It prevents you from getting it. Not 100%, but you are much less likely to contract it if you are vaccinated.
2. It prevents serious outcome. Once again not 100%, but you are less likely to die or wind up in ICU if you do contract it.
3. It prevents you from spreading it. Once again not 100% but because you get less sick, you are less likely to give it someone else. (Smaller viral load)