People including scientists make misstates. Science is based on evidence and when new evidence becomes available the science is updated.
You are partially correct that CDC Director Dr. Rochelle Walensky initially made a statement suggesting that vaccinated people do not carry the virus or transmit it to others. It would be wise of you to take this as a learning lesson so as not to repeat it over and over, I doubt that you will.
However, the CDC later clarified that while vaccinated individuals are highly unlikely to transmit the virus, the evidence isn't clear, and they are continuing to evaluate the evidence
Therefore, while vaccination significantly reduces the risk of virus transmission, the CDC has not definitively stated that vaccinated individuals cannot transmit the virus.
While pointing to other peoples mistakes you might do yourself a favor and recognize your own.
BTW, I am not a fan of the the CDC. Here is something that they were definitely wrong on and have not yet corrected. The CDC does not fully recognize Covid as being airborne.