I do think there is definitely such a thing as "clashing personalities" - people who will never get on.
Our oldest, Liam, is now 4.5 and since going to nursery he's had to be kept apart from another little girl because they just don't get on and always end up in a big argument. No one knows why but just know to keep them apart. They both play fine and get on with all the other kids but for some reason really annoy the hell out of each other (in 15 years they'll probably get married).
The fact is, there are some people that for whatever reason, we don't get on with or have got off on the wrong foot with or there has been some misunderstanding at some point which has since been long forgotten but the 'fight' continued.
In these cases I think the best solution is death by firing squad.
he he he
I'd love to post something like that for real one day, lol.
Seriously, I think the best solution is to ignore each other **unless** discussion can be kept on what is being discussed and not "well x once said".
Easy to say ... hard to do (I know)