My jogging partner is getting tired, so I'm going to run faster so he can't keep up.
Why do you want to leave your jogging partner behind?
I want to be the fastest one
You should not be so competitive, especially when it comes to your friends. It may feel good to come in first, but you are supposed to be helping each other to work out, not to win. Try to be patient with your partner.
I don't have time for this. He knows I have to prove him wrong by being the fastest, this shows I'm better than him.
This only shows that you are better at jogging than he is, and it does nothing otherwise. Your partner probably agreed to jog with you because he thought it would give you both the motivation to keep going. You are just making his workout harder by leaving him behind, and not really accomplishing anything.