The vaccine was a tremendous scientific achievement and it has undoubtedly saved thousands of lives (hundreds of thousands? maybe).
However, it was rolled out with insufficient data to make the claims that were made about it. There was simply not enough data to make the claim, as was made by people including Biden, that the vaccine would eliminate the risk of infection. It turned out that this was not the case. The efficacy of the vaccine with regard to prevention of infection wanes much more quickly than what was hoped for at the start. Since then, we have learned that the vaccine still protects against serious disease even if it doesn’t offer much protection from infection.
So, incorrect claims were made. People see that. They are not idiots.
The proper course of action for the public health community would be to say something like: “The vaccine did not live up to our initial hopes with regard to the prevention of infection. However, we have been gratified that the vaccine has proven to be very helpful for the prevention of serious disease among the infected. In retrospect, we did not have enough data to make the claim that people would not catch Covid if they were vaccinated. The reason for that is that we wanted to get as many people vaccinated as possible before we waited to see the long-term effectiveness of the vaccine against infection.”
Be truthful and transparent and people won’t form so many conspiracy theories.