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I'd point out that by recounting your personal experience and bringing up your coworkers, you essentially admit to this being one of your errors in logic.
You act as if your personal experience is "the average" when in reality you are an edge case who was able to suffer an infection unvaccinated, with mild symptoms. That's rare.
Others, like your coworkers, may have needed the vaccination just to survive, because without it they would have suffered symptoms severe enough to kill them.
You can't know. And the statistics, which you can't determine based on personal experience, say that's exactly how it works. That the vaccines saved millions.