Your direct reports don’t get to choose whether or not you’re going to be the boss. But they do get to choose whether they want you as their boss. If they have the strengths you need and fit with the culture you’re trying to build and want to be part of the team, great. If not, make them go away.
This is about people who did not get a promotion they hoped for. Whether one of their peers is promoted into the position or a new leader is brought in from the outside, they feel that the new leader took “their” job. Some decide that the new leader will be good for them. Some never get over the sense of loss and choose to undermine the new leader so they can take their job themselves. If you’re that new leader, you need to figure out who’s in which camp.