[AltarEgo]

To me the essence of the word "race" as it's used in the terms of a definition of this kind of context, is that it's a competitive endeavor. If you're entering road races then that is the way that you want to run them. For the purposes of trying to do your best against everyone else who's also in the race as well as even yourself. Because even if it means that you don't finish ahead of half the field you may still run a personal best time over a course and then you achieve a sense of accomplishment and pride.
You can't do these sorts of things if you simply keep pace with your friend. These are concepts that your friend needs to at least know about and then allow you the freedom to try and enjoy.
Training is something entirely different if you want to have company on your run. Like g_samsa said, you should have a talk with your friend and let them know how you feel about these things. The friendship should be able to last in spite of the two of you not racing together.