The Bible tells us about a leader like that. The apostle Paul wrote a letter to one Diotrephes asking him to engage in debate, and the church leader refused. According to the text Diotrephes 'loved the pre-eminence' or 'loved being first' and felt he was above entering into debate with anyone, least of all Paul. Truth be told, he was probably afraid that he might lose that theological contest and so refused to budge, but the real reason was arrogance. In the case of a previous UK Prime Minister, Margaret Thatcher, a very similar haughtiness preceded her political downfall. "Pride" as the saying goes "precedes a fall".
I don't expect either my consultant or the Prime Minister will suffer any great consequences from not being willing to answer questions and debate their position, but after a lifetime of leadership roles within the church, I hope for better things from Christian leaders. Diotrephes is a very poor role model for Christian leaders, who should always be ready to give an answer for the faith that is within them, for their conduct, and for the sacred charge that is given to them by the Lord. Any leader who finds him or herself loving 'being first' should note the example of Jesus who washed his disciples feet and declared that they who desire to be first among us should be servants of all. That is a long way from the kind of leadership we see in the worlds of politics and medicine, but we are entitled to expect better of those who lead the church.
