Why were Fred and George separated during the battle?

I've found this to be quite odd that they weren't together when Fred was killed. You'd think after George losing his ear when they were separated earlier in the book that they'd try to stick by each other's side as much as possible.

I get that in a battle it would be hard to stick together, but at the time of his death Fred doesn't seem concerned that he doesn't know where George is.

For a while I've had this theory. After George lost his ear, Fred became more protective of him. While they mostly still got along, George didn't entirely like this new protective side of Fred. Come the battle of Hogwarts, he insisted that Fred let him go into the battle on his own. Fred made the hard decision to allow George to go into the battle without him, which came at a price that neither of them were expecting.

I don't know if this was ever intended to be the case, I might just be overthinking it. But it makes more sense, given the context of what happened earlier in the book.