It's mainly a lack of studies as transmission is outside the scope of clinical trials. They only assess efficacy and side-effects, they do not even consider transmission. Based on the logic below, you could still spread after vaccination even if the antibodies are helping to protect you from severe symptoms.
In short, the vaccine may be pushing most people to asymptomatic infection. Still infected, still spreading, just not dying. There have been insufficient studies to determine how the vaccine is affecting infection and therefore transmission to determine any possible effect. As the studies progress, there could be a substantial difference in transmission between vaccines (especially AZ vs Moderna/Pfizer as their mechanism of action is very different).
Clinical trials did not test whether a person could still spread the virus to others after receiving the vaccine.
www.cbsnews.com
"We don't have the clinical trials to show that people who are vaccinated are not shedding the virus," Dr. Dyan Hes, founder of Gramercy Pediatrics in New York City,
told CBSN. "They might not be getting sick, but they might still be shedding if they got it."
Dr. Joel Ernst, an immunology and infectious disease expert at UCSF, said that "in the absence of any other information," it's safe to assume that "having antibodies won't protect you from shedding the virus.
There are still important unknowns about how Pfizer’s vaccine and others will work once they get injected in people around the world.
www.sciencenews.org
What’s more, neither the Pfizer nor the Moderna vaccine trials tested whether the vaccines prevent people from being infected with the virus. Those trials, instead, focused on whether people were shielded from developing disease symptoms. That means that it’s not clear whether vaccinated people could still develop asymptomatic infections — and thus still be able to spread the virus to others.