It is not correct to say the vaccine doesn't work, on the contrary they would not be mandating it illegally and trying to force everyone to take it if it didn't work.
The issue is that the effectiveness of the vaccine comes at a very high cost.
1. The MRNA vaccine operates by instructing your immune system to make specific antibodies against the Covid virus. For example, it might make specific antibodies against the spike proteins. As a result this causes the mutations without those proteins to be most successful, and since the Covid virus can mutate rapidly within six months you need a new shot, a booster. This process has continued again, and again and again. Every time your body is making these specific antibodies that will stop this one virus if it spots it. In this sense it does work.
2. However, there is a very high cost. Your body has general antibodies that can fight any foreign body and it has specific antibodies designed for one specific virus that might have caused you to be sick in the past. What the vaccine does is hijack your immune system to focus on making the specific antibodies while not making the general immunity.
The analogy that those who invented this approach use is the Magino line. That was a wall of concrete with large guns put in place. It was made by France and went along their border with Germany. It was impenetrable to German tanks and it worked. The problem was Germany simply drove around the wall through the Ardenne forest and entered France from the side.
The vaccine does the same thing, it overemphasizes the risk of Covid to the expense of your immune system being able to fight against any other attack. One shot only weakens you a little and that will wear off over time. But with each shot your immune system is weakened more and more. The shots and the boosters are giving you "acquired immune deficiency". It is very clever because now when people die they die from everything but Covid (for the most part).
The best example is China where everyone was required to get every shot.