These days, leaders gain respect through consistent trustworthy behaviour. Many leader aren't granted respect simply because of their authority position. They have to earn it through their actions, words and behavior.
In other words, it's a lot harder to get respect because you have to spend time nurturing relationships. Given this relationship currency requres work, what is the cost of the difficult person who is undermining that trust on your team?
The cost can be seen in multiple ways as trust is undermined and teams fall apart. Undermining authority is usually intentional and deliberate, so leaders need to be aware of it.
Difficult attitudes are contagious, spreading unanticipated consequences throughout your workplace. Difficult people can complain about you when you aren't aware. If they do it often enough, it makes it harder for a leader to build people faith.
Difficult people can misrepresent your attitudes or actions and be secretly undermining your authority. Going around your back, advancing a hidden agenda, making false accusations all undermine your authority.
The squash the dissent, it helps to face it straight on. Ask the underminer to what they said and why. Eventually, by checking facts and conversations you can straighten out the conflict and catch the undermining culprit in his tracks.