- Wolverine dies;
- One half of Wolverine rebuilds itself into Wolverine, the other half rots;
- Both halves of Wolverine rebuild themselves in Wolverine;
- Both halves of Wolverine attempt to rebuild themselves, but only one is actually Wolverine, the other being some messed-up nightmare creature, or something.
So if we assume it can't be as simple as picking the "regrowable" side, earthworm-style, what does that leave us? If, for example, we were to clone Wolverine (and then cover that clone's skeleton with adamantium), and immolate opposing halves of each of our two Logans, we'd surely end up with two Logans again fairly quickly (and, as a result, half the already meagre life-expectancy of our fearless lab techs). What's the difference between that experiment and a lateral bisection?
I think the only real explanation is some kind of hand-wavey nod to the soul, or perhaps in more secular terms, Logan's will to survive. He can survive losing either half of his body, but if he's chopped in two, one side will somehow want it more, and become the true Wolverine, whilst the other becomes something different. You still get two people, or two life-forms, depending on how you look at it (option 4 above would be the most obvious choice of how to run with a bisection actually occurring in the comics, which is certainly not to say trying it would be even a remotely good idea). You could even surrender to cliche and give each half different traits from the original. Indeed, Wolverine & The X-Men: Alpha and Omega already gave us one suggestion, albeit under very different circumstances, featuring as it did a rational but amnesiac Logan and a drooling violent animalistic Wolverine.
In that respect, "only one Wolverine" makes sense as a summary, albeit whilst making no sense at all as an actual logical position (and yes, I'm aware that applying logic to superhero comics is inherently ridiculous; but if you don't find it fun nonetheless, then frankly I rather pity you). Me, I'd go for option 3, and damn the torpedoes. Hell, do it right, and for the first time in twenty years Wolverine's appearances across the Marvel line might actually make some sense.
(X-posted at Musings of the Cosmic Calamari)