If you want to draw the line in that way, then break it all the way down and apply the principle evenly. Every single time you change your mind in any way, shape or form, that is an ever-so-slightly different you. The difference is so minor that it's basically no difference at all, but it does exist.

So, when you decide to put stawberry jam instead of grape on your toast, that old you that used grape is dead. And then the next day, when you go back to picking grape, the stawberry you is now dead and the grape you is resurrected.

Obviously I'm exaggerating with such an innocuous example, but the basic principle applies. It's all arbitrary, from a truly objective perspective.

There's a number of deductions one could draw from this, but a big one is that we try to apply identity as if "things" are real, but it's mostly just our choices, which can vary as much as we want them to. This goes against a natural human desire for stability, we kinda wish that once we learn something, it can "stay learned". But that's just like Mr Incredible complaining that his city won't "stay saved" in the beginning of the movie.

Pluto's recategorization away from planetary status triggered this in a lot of people. It's arbitrary though, we made those decisions in the first place. And in the modern world, we really need to be ready to handle new stuff all the time, so flexibility is important.