To effectively persuade others, a leader needs to engage people on multiple levels. Aristotle articulated this as ethos, pathos, and logos. But, even if people agree that change is necessary in the abstract, they'll instinctively resist.
Change has no constituency.
- Jack Welch
If you don't carefully manage team morale, the change you want may never happen. Because inertia jumps dramatically as morale falls, the onus is on leaders to set the stage for success. This might mean mentally preparing people for painful upcoming changes. Or, this might mean altering the rules of engagement, to clearly establish a new leader's authority. Regardless, frame the discussion so people understand the change's importance, not just to them, but to the organization as a whole. If they don't understand the broader context, how can you expect them to help you win over your skeptics?