This is the correct answer. Before Linnaeus, there were lots of different classification systems. (Genus and species goes back at least as far as Aristotle, but morphological comparisons really weren't a thing until the 1700s. So you could characterize humans as "featherless bipeds" or as "rational animals", but there wasn't a systematic method of characterizing all living things. And it's pretty obvious that limiting yourself to just genus and species is of extremely limited utility. Especially if you have a plucked chicken.) Linnaeus proposed a method of grouping similar to similar. The method was essentially "look at everything, and if it's mostly the same, they're closely related, and if it's almost entirely different, they're not related at all".

Even-toed and odd-toed just happened to be something that indicated all the other stuff really, really well. (Among ungulates.)