There are a lot of subtleties. Ring species are a particularly fun one: you can have a population that live around some natural obstacle (like a large body of water) where individuals can breed successfully with individuals near to them but not with ones further way (like directly across the barrier), in a continuum of variation.

"Ring species are a particularly fun one"

This is really interesting, thank you. I've never heard of "ring species" before.

Thought experiment. Three populations, A, B, and C, divided geographically along a line. Individuals from group A can breed successfully with those from B but not with those from C. Individuals from group C can breed successfully with those from B but not A.

How many species are there? This is why the term "species" can never be entirely objective. I remember the eureka moment I had when I finally understood this (admittedly somewhat simple) point.

It can even be more subtle, it's entirely possible that some rare members of A can C breed, and some members of C and B would not be able to breed. The "fertility" relation can only be decided between two individuals, not groups. Group-level fertility is a statistical average of individual fertility.

That said, I don't think that means that "species" is entirely subjective or meaningless.

Even within one species, not every individual can successfully breed with every other.

Is that based on a real example or hypothetical?

Polar bears can have furtile offspring with grizzly/brown bears. See: https://en.wikipedia.org/wiki/Grizzly%E2%80%93polar_bear_hyb...

the reproductive incompatability, is based on physiological range.

in general, there are multi organizational levels of reproductive incompatability.

in this case, the geographic distance, orogenic blockade, and ecological confounds of arctic conditions preclude easy mingling of U.arctos x U. maritimus.

Interfertility is not an equivalence relation, does not form equivalence classes https://en.wikipedia.org/wiki/Ring_species

Sometimes it’s hard to objectively tell whether two animals don’t appear to reproduce because they are unable genetically, or technically able still but behaviorally unwilling in normal natural circumstances, or we don’t know but we just haven’t observed it for that particular combo, etc

if I'm not mistaken some human populations have neanderthal DNA which indicates that humans had reproduced with them and created fertile offspring. outside of that example there are a ton of species that can produce viable offspring like dogs, wolves and coyotes.