"Although wizards are advised to avoid being seen by their past selves. If you're attending two classes at the same time and you need to cross paths with yourself, for example, the first version of you should step aside and close his eyes at a known time - you have a watch already, good - so that the future you can pass. It's all there in the pamphlet."
"Ahahahaa. And what happens when someone ignores that advice?"
Professor McGonagall pursed her lips. "I understand that it can be quite disconcerting."
So what does happen when someone ignores that advice, on the assumption that history with time-travel is self-consistent in the way EY describes?
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Probably nothing, but it would require a series of improbable coincidences (every atom in future!Harry needs to be in the same position that past!Harry saw it in), significantly complicating the loop. Such complications would make it simpler for the loop to not happen at all, and so it probably wouldn't. A precommitment to interact with your future self as little as possible would then maximize the probability that the loop occurs in the first place.
So what do you think McGonagall meant by disconcerting?