For more robust immunity, many people do this.
(To catch it once is unfortunate...)
No, your friend didn't have COVID a second time after being vaccinated after their first infection. Especially lacking any clarification that they were in fact tested positive both times, you are merely contributing to noise on the internet.
1) "a friend of yours" is not a data point on which others should base their worldview (unless their testicles got huge and their fiance called it off, why even share?)
2) reinfection is rare
3) it is likely the first time they think they had covid, they weren't tested, and actually had the flu.
Here is the CDC information on reinfection: https://www.cdc.gov/coronavirus/2019-ncov/your-health/reinfe...
As of August 6, 2021, the CDC has nothing conclusive to say on the matter: "Cases of reinfection with COVID-19 have been reported, but remain rare . "
Anecdotes are noise, and I would encourage you to do no further research.
PCR tested positive both times, double jabbed in-between. You might not like the fact that it's possible, but that doesn't make it impossible.
1) You seem to be the one projecting a world view based off an anecdote. Chill.
2) Law of large numbers. A small percentage of a very large number is still a large number.
3) Here you go again with made up "facts" that aren't even anecdata.
> Cases of reinfection with COVID-19 have been reported
Seems pretty conclusive. They're referred to as "breakthrough cases", and not as rare as you seem to believe. What's more important is that the risk of hospitalization and death in breakthrough cases is considerably reduced.
> I would encourage you to do no further research
I would encourage you to do more. Making up "facts" to make a point does nothing to strengthen your position (whatever that may be – seems more like you just wanted to rant).
It does mean that your body is prepared to sweep the virus out faster and prevent it from spreading as far in your body.
In computer terms, a vaccine reduces the latency between when your body gets a virus and when it reaches critical immune response to get the virus under control.
So, for example, while you may get Covid in your nose, being vaccinated means that it doesn't get down into your lungs and heart and cause damage down there (the issues that cause most people to be hospitalized).