One Fundamentalist quarrel is that marriage is compulsory for Church leaders. For Paul says a bishop must be "the husband of one wife," and "must manage his own household well, keeping his children obedient and respectful in every way; for if a man does not know how to manage his own household, how can he care for God’s Church?" This reveals that only a man who has obviously looked after a family is fit to care for God’s Church; an unmarried man someway untried or unproven.
This explanation leads to understandable silliness. For one, if "the husband of one wife" really meant that a bishop had to be married, then by the same logic "keeping his children submissive and respectful in every way" would mean that he had to have children. The theory that Church leaders must be married also opposes the clear reality that Paul himself, an important Church leader, was solo and happy to be so. The suggestion that the unmarried man is somehow untried or unproven is equally ridiculous.