I agree that comparing to others is mentally unhealthy. This applies not only to the gym/fitness but all areas of life. On the other hand, measuring progress is a good motivator, and I feel a proper way to do that is to challenge yourself. If you were able to shave X seconds off your mile time, or improve your squat weight by Y pounds, then I feel it is a proper motivating factor as well as one that could assist in keeping your mental attitude in the right place when other facets of your life are troubling.
I believe comparing yourself to others can be healthy, as long as you don't let it get out of control. How else do you know what's possible? If your friend is progressing much faster than you, almost certainly he is doing something different than you are. If you weren't keeping track of him as well, you might miss out on chances to improve.
If everyone was just racing against themselves, I really don't know that we'd ever have seen a 4-minute mile.
