I totally agree that it is fun to have someone to shoot with, not necessarily against but for mutual improvement in your shooting abilities. I have shot a lot of competitions but to me a competition was primarily me shooting against myself. In perspective, in military competitions I was always at the top of the list of winners, and sometimes even managed to pull a win out of my butt. My strong points were offhand shooting (both rifle and pistol) and 600 yard long range shooting across the National Match Course. Military matches all required service rifles and pistols, but also competed in many civilian matches where the service rifles and sometimes pistols were not as competitive as those shooting match bolt action rifles or pistols built specifically for competition. I usually did well, but usually not anywhere near the top of the winners list in civilian matches. Did that bother me? Not at all simply because regardless, I always shot against myself, looking to see how I could improve my scores under pressure, which competition added pressure not there when shooting practice. So now you are asking how does this relate?
I have been an instructor for a long time. I have taught a lot of people, both military and civilian how to shoot. One of my greatest joys in life is when a student outshoots me, does better than I do. It makes me smile and gives me a warm fuzzy feeling. I have had a few ask me if it upsets me that they are now shooting better than I can. My answer is always that it doesn't bother me in the slightest. My success is in guiding others through the myriad of obstacles that cause people to not excel when shooting.
The hardest competitor that you will ever shoot against is yourself. If you go to the range with the idea that I am going to do better this time that I did during the last range session, be it practice or competition you will be well on your way to success. Conversely if you have hit a plateau, or are having issues do not hesitate to ask for help. Remember, the only dumb question is the one you don't ask.