That you anecdotally know vaccinated people who got Covid and that Covid vaccines lower the chance of being infected with Covid can both be true?

Yes, I knew I would get called out for an anecdote on this website. Thanks for not disappointing.

Perhaps you shouldn’t knowingly use flawed arguments if you don’t wish for the flaw to be called out

Meanwhile, among the many people I know who have been vaccinated, there's been just a single breakthrough case, and that case was due to catching covid from an unnvaccinated co-worker.

Since you seem a bit confused, here's what we know and don't know AFAIK:

1) Vaccination reduces your chance of getting infected. The efficacy depends on the strain of covid and the vaccine, but I have yet to see any science indicating that any vaccine has no efficacy against any strain.

2) Vaccination may or may not reduce your infectiousness while you are sick

3) Vaccination does reduce the average duration of infection, which means that while you may be as infectious as a non-vaccinated person while you are sick, you have a shorter window in which to spread that sickness.

So despite the unclearness of #2, we are very clearly able to say that vaccines reduce transmission because of #1 and #3.

Thanks for the assessment, but I'm not "confused" at all. Maybe if the pro-vaccine-mandate crowd wasn't so snide and insufferable people might take you more seriously.

Where do you see me advocating for vaccine mandates?

If there is a part of my comment you found snide, please let me know as that was not my intent.