We often point to competition as a tool to bring out the best in people. You will run faster or work harder or fight more ferociously if there's someone breathing down your neck or a record to be broken.
The problem with competition is that it takes away the requirement to set your own path, to invent your own method, to find a new way. When you have competition, it's the pack that decides what's going to happen next, you're merely trying to get (or stay) in front.
Competing with yourself is more difficult, requires more bravery and leads to more insight.