Used when someone won't easily give up, showing determination to have things a certain way. He insists on doing the presentation himself, despite the team's offer to help.
Pro Tip 2/3
Slight annoyance
May imply that someone's determination is causing irritation or inconvenience to others. She always insists on doing everything her way, which frustrates her coworkers.
Pro Tip 3/3
Moral conviction
Can reflect a deep belief in personal principles or values guiding someone's actions. He insists on doing the right thing, even when it's not the easiest option.