When a couple breaks up (dating, marriage whatever) do you think it’s rude or invasive to ask why?

That depends upon a lot of factors. How close of a friendship would be a primary factor. But many other things like time & setting. It would be inappropriate to ask in the presence of others, or at work. My wife & I have been separated for 6 months. Some of my closer friends know, but others don't. I told my very CLOSEST friends. Oddly, some of my other friends KNEW, but didn't actually ASK. So, they made leading statements IN CASE I WANTED to tell them, which I DID. They meekly said that they "had heard about it", but didn't want to pry.