I don't know what it is about the gym that brings out the competitor in people.... The only purpose of going there is for
your own health. You're not there to look tough in front of your friend or anybody else!
That said, I sometimes have to watch myself--when I get on the elliptical trainer machine next to a hot girl, I always seem to want to race her...
The guy who introduced me to my gym gave me the following advice: "Do NOT try to compete with the woman on the machine next to you! She'll beat you down, spit on you, and leave you for dead!" He cracked up a whole row of girls-on-treadmills with that one.