Example: https://www.medrxiv.org/content/10.1101/2021.03.06.21253051v...
"Out of 149,735 individuals with a documented positive PCR test between March 2020 and January 2021, 154 had two positive PCR tests at least 100 days apart, reflecting a reinfection proportion of 1 per 1000"
So that's really incredibly low. Note that this paper, like so many others, assumes a false positive rate of zero: with such a low number of reinfections they could easily just be testing errors and thus the reinfection rate can easily be even lower still.
Remember - COVID is a mild disease for the vast majority. Having been infected reduces your chance of infection so low that it takes you from a very low chance of having serious problems to "you need scientific notation to express the probability of having problems". Vaccines can only make things worse for those people, not better.
Unfortunately our society has completely lost all rationality over vaccines. Your so-called infectious disease expert is a great example of that. Firstly, he's dead wrong that vaccine-induced immunity is longer lasting. It lasts months at most, which is why even vaccine-pushers have given up claiming it stops you getting COVID. And antibody titers are not the end goal here! The goal is to avoid getting sick. They've completely substituted the means for the end, which is the sort of contempt-worthy irrationality that makes people reject the vaccination programme.