This kind of thing is repeated often, but I don't think it's true. For one thing, how would tattoos last so long then?
More relevantly, I don't think neurons are replaced. There must be some material churn in the atoms and molecules that make them up, but even then different for different molecules - e.g. I don't know how much of our DNA molecules get replaced over a lifespan from the repair or other mechanisms.
The "on average" is doing an awful lot of work. Some cells are never replaced, some organs are replaced every few years or even partially over decades, some organs are replaced every few months (one of which is the skin).
Tattoos however, IIUC, sort of "float" between cells, and as those cells are replaced one-by-one the ink is kept in place by the surrounding cells that are still there.
> how would tattoos last so long
Answered by Kurzgesagt: https://www.youtube.com/watch?v=nGggU-Cxhv0
I suppose tattoo ink isn’t all in the cells. I’d guess the ink within intracellular spaces is never removed by the body (or very, very slowly).