Seeing everyone as your competitor has two negative consequences. First, it isolates you and your efforts, putting a full burden on your shoulders that others could help you bear; and second, it means you waste energy trying to set others back rather than using that energy to push yourself forward.
Consider the following true story by Frank Koch in an issue of Proceedings, the magazine of the United States Naval Institute. Two battleships assigned to the training squadron had been at sea on maneuvers in heavy weather for several days. Koch was serving on the lead battleship and was standing watch on the bridge as night fell. He recounts his experience.
The visibility was extremely poor with patchy fog, so the captain remained on the bridge, keeping an eye on our navigation activities.
Shortly after dark, the lookout on the wing of the bridge reported, "Light, bearing on the starboard bow!"
The captain called out, "Is it steady or moving astern?"
The lookout replied, "Steady, captain," which meant that we were on a collision course with that source of light.
The captain then called to the signalman, "Signal that ship: We are on a collision course... advise you change course 20 degrees."
Back came the signal from the other ship. "Advisable for you to change course 20 degrees!"
The captain barked, "Send, I'm a captain... change course 20 degrees immediately."
"I'm a seaman second class," came the reply. "You had better change course 20 degrees!" By this time, the captain was furious. He spat out, "Send, I'm a battleship. Change course 20 degrees."
Back came the signal from the flashing light, "I'm a lighthouse."
The captain changed course.
The moral of the story is that it is futile to try to set others back when you could turn yourself 20 degrees and go forward!
Source: Psychology of Motivation by Dr. Denis Waitley
My two-bit: Another aphorism is, "pick your battles". There are contests worth fighting even if the odds of losing are high, and there are contests worth avoiding even if the odds of winning are high.