I can think of two things.
The first is a bit morbid, but consider what happens if some country ever decides to weaponize space. Being able to have people up there who can use the weapons available to them and exercise their independent judgement even in the face of an earth-to-space communication failure is important. It's the same doctrine that's behind ballistic missile submarines equipped with nuclear warheads.
The second is less morbid-- the colonization of other planets. This is necessary to protect the human species from an extinction event. Maybe even one that resulted from the aforementioned submarines. Naturally in order to colonize other planets we need to study the effects of space on humans. In order to do that we need to send them into space.
All of that said, I also believe most of our current missions can be done much more cost effectively by changing them to unmanned missions. But you can't take your eye of the long game, which just like the rest of history, is manned and involves militarization and colonization.