The most common response I've heard from people who believe the government lied about the COVID vaccine is that they take issue with the word 'vaccine'. They think it should not have been described as a vaccine since you can still get COVID after getting the vaccine, and the vaccine has a certain timeframe after which it loses efficacy because the virus mutates.

Pointing out that other vaccines have these exact same properties just leads to them claiming all of those are not really vaccines and we need to stop recommending them. In their mind if its not a shot you get once, after which there is no possibility of contracting the disease, it is a hoax.

You can see exactly this train of thought in this thread from some people