Genetic analysis is great! It’s really helpful! But it’s not a cure-all. Genetics help figure out where the lines are between taxa. If the distinction is clear – if the taxa have been separate for a long time – genetic analysis can find the difference. But in most (not all) cases, morphology can find that difference, too. Where morphology gives unclear answers, genetics may – or may not.
In the unclear cases, genetics provides more evidence but it can’t give us simple answers because there are no simple answers. Two populations are diverging, becoming two species. Will they continue? Will they merge back together? At what point should we call them different species? Genetics can’t answer those questions.
Two populations are similar but differ slightly and don’t interbreed because they’re geographically separated. They probably would interbreed if they met, but they don’t meet Should they be called one species or two? The answer must be a matter of human judgement, nothing else. Genetics can’t provide the answer.
People sometimes seem to think that a certain amount of genetic differentiation makes two populations different species. That isn’t true. Sometimes a small genetic difference or a chromosome rearrangement with little genetic sequence change causes two populations to be reproductively isolated. In other cases, a single species with clearly interbreeding populations is genetically variable.
We treat species like nice, neat, mutually exclusive categories because that’s what we need our words to be. Animals, plants, and other organisms have no need for our neat words. Our learning to analyze genetics doesn’t change that.