Not sure of all the details of this fuckery, but the causes of action the plaintiffs are alleging are breach of fiduciary duty, negligence, fraud, and intentional and negligent infliction of emotional distress.
The general premise of their arguments is that as an influential and powerful Pastor and spiritual advisor, Mr. Long had a controlling influence over the plaintiffs' conduct. He had a fiduciary responsibility to act in the best interests of those he had an immediate and direct influence over. By engaging in sexual acts with the plaintiffs, Mr. Long breached that duty and as a direct and immediate consequence of that breach, plaintiffs suffered severe emotional distress.
With regards to 'duty of care', a fiduciary duty is the highest level of trust and responsibility. One who owes a principal a fiduciary duty has to ensure that the principal's interests are best served.
This situation can also be described as "Pastor Malpractice" since legal malpractice cases are probably what lay people can analogize with what Eddie Long did wrong legally.