Not sure what you're looking for, and this answer probably isn't it, but I think you're looking for something that is doesn't really exist in any meaningful sense. I think you're looking for a 100% waterproof definition without any corner cases, one that would allow you to definitively counter someone who says "it's a spectrum" etc.

I'm not a biologist, but my understanding is that biology isn't a thing where you can meaningfully have that. You cannot find such a definition for what a species is, for example — or life, for that matter: when does a chemical reaction become "life"?

You can tell that cats and dogs are different species, but what about a population of a species that used to be one unit, but now has split into two, maybe for some geographical reason — let's say an earthquare opened a chasm that split the population in two and now they can't get to each other any more. Over time they will start evolving apart based on chance that's a part of evolution.

So when do they form two different species? Is it at the point when they can't make fertile offpring anymore (even though they might be able to make infertile offspring)? Is it at the point where they could make fertile offspring (by way of insemination in a lab for example), but in the wild they won't, because their mating season or mating rituals have changed so much that they don't "recognize" each other as potential mates? Etc.

I don't think there's a "gotcha" style answer to the question, and I think your question is similar. In any case these things will never be resolved through logical argument on this level.

But this cuts both ways. Of course anyone, who argues that in order to have a case for sex at all you need to have a 100% waterproof definition with no corner cases, has equally misunderstood what the phenomenon they're discussing is about. There's always going to be room for choosing — opportunistically or not — to emphasize the "islands of stability" (Stephen Jay Gould's term) on the one hand, and "it's all fuzzy" on the other.