Virtually nobody really uses that definition of species because it’s totally untenable in practice - you’d put every species of wolf, dog, and coyote in the same bucket, for a simple example, but it gets much worse than this. Ligers are sometimes fertile, are lions and tigers the same species? Are vast swaths of the current catalogue of hominids the same species? When you get into fish and birds this becomes even more nightmarish. Let’s not even talk about plants. Further complicating this is that “ability to interbreed” is not even transitive!

Or consider looking at it from the other direction - it only even seems to make sense if you have some preconceived notion about species anyway. If two humans are infertile or have an infertile child, does that make them different species from each other? Of course not.

I’m not making a novel argument, Darwin goes in-depth on this very topic in the Origin of Species.

“Species” and “ethnicity” (to which “ancient Roman” belongs) are in fact identical concepts; the only difference is the zoom setting on populations, which in both cases varies for any specific example but generally is farther out for species and closer in for ethnicity. In both cases they are arbitrary lines drawn around real clustering of population genetics.