Looking at a specific problem for a short period of time (10 minutes) with another competent programmer is one thing. But trying to concentrate with another person looking over your shoulder is aggravating. My experience is that you are more likely to take shortcuts to get the task over with. You don't want to do anything that is going to take real concentration because concentration is impossible when another person is likely to interrupt your thinking to converse. That is by far the worst part of pair programming.

Knowing that your mind is free to explore a problem to whatever depth is necessary is absolutely critical to solving something non-trivial.

I find it really hard to explain the damage of interruption to non-programmers. Whether it is a girlfriend or a client that likes to talk while you're fixing their bugs. I don't think it is necessarily unique to our profession, but it is certainly rare enough that most people seem not to get it.