As a former marine I’m obligated to make the obvious point that while of course the USMC thinks it is better than the Army, marines think that because it is true a randomly selected marine is better at war fighting than a randomly selected soldier. A marine logistic company does not make a “wrong turn” in the middle of a war zone, ie, Jessica Lynch convoy. And the opening captions in Black Hawk Down point out Adid attacked US forces only after marines left. The USMC is about war fighting with a smaller organization and narrow focus, while the Army has a broader mission.
Second, it is not true that US marines believe they are better than everyone else as they will readily admit the Royal Marines are hands down the best light infantry in world.
Bottom line: evidence is a sign of evidence, not elitism.