#3 He wanted to fire Edge back in 2005
Edge had a very successful run in WWE within a span of 15 odd years and 11 World Title wins before succumbed to his injuries and left WWE in 2011. If Triple H, however, had more power over the company in 2005, Edge would have had to retire sooner.
The more astute of you would probably remember that the real-life disputes between Matt Hardy and the Rated R Superstar had caused a lot of tension in the locker room and Trips wasn't having any of that.
Corey Graves deleted his Tweet! More details HERE.
Triple H rallied the entire roster to try and convince Vince to fire Edge for breaking the sacred code of WWE locker room. In the end, though, McMahon chose to fire Matt Hardy; albeit for a brief period until he was re-hired due to a public outcry.