A leader can disappoint people and still make a responsible decision. That observation needs a second question: how can the people affected tell whether the decision deserves their trust?
Being unpopular provides no proof of courage or good judgment. A choice deserves scrutiny whether it receives applause or criticism. The useful test is how it was reached, whose interests were considered, and what happens when its consequences become clear.
Explain the competing responsibilities
Leadership becomes difficult when reasonable needs conflict. A team may want a deadline extended while a customer depends on the original date. A public service may face requests that exceed the resources available. Simply declaring a decision “necessary” leaves the people affected without enough information to assess it.
A clear explanation identifies the problem, the realistic alternatives, and the reason for choosing one. It also acknowledges who bears the inconvenience or loss. People can disagree with a conclusion while understanding how it was reached.
The published overview of The Ask's conversation with Julie Mayfield includes listening to constituents with conflicting priorities and making decisions without an obvious answer. Those are useful starting points for discussing responsibility in practice.
Give criticism somewhere to go
A leader who expects disagreement still needs a way to hear it. A decision can be principled and based on incomplete information. Someone closer to the work may see an effect that the person making the decision missed.
Useful questions include: Which objection concerns a preference, and which identifies a practical risk? Who has not been heard? What evidence would change the decision? Answering those questions makes room for challenge without requiring unanimous agreement.
Listening also creates an obligation to respond. If an objection cannot change the outcome, explain why. If it reveals a mistake, acknowledge what will change. Inviting feedback and then ignoring it makes the invitation difficult to trust.
Separate a principle from a preferred method
A principle might be treating people consistently or keeping an agreed commitment. The method used to honor it can often change. Confusing the two can turn a reasonable concern into an unnecessary contest over authority.
For example, a fictional team manager may need to protect time for urgent customer work. A rigid meeting rule is one possible method. Moving a meeting, changing who attends, or replacing it with a short written update may serve the same purpose with fewer costs. Revising the method can strengthen the original commitment.
Return to the consequences
A difficult decision remains the leader's responsibility after the announcement. Set a point to review whether the expected benefits appeared and whether the burdens were greater than anticipated. Give people a practical route to report problems.
It is reasonable to ask whether a leader can withstand disapproval. It is equally important to ask whether they can explain themselves, correct an error, and remain accountable to people who disagree. Those habits give an unpopular decision a better basis than confidence alone.
For the related question of supporting someone without promising what you cannot deliver, read Why Helping People Is Not the Same as Wanting to Be Liked.