A lawyer represents a client in court. An accountant prepares taxes for a client. A director manages a trust for the beneficiaries. There is no doubt who is being represented in these cases. Loyalty is easy to determine.
Confidentiality is easy to understand.
The problem comes about when a lawyer, for example, wants to represent both sides of a lawsuit, or an account wants to represent both the IRS and the taxpayer in a dispute. In cases with inherent conflict of interest, it is very hard to be a dual agent. It is hard to be loyal to both sides, to get the best deal for both sides, to keep both sides positions confidential. In some cases, such dual agency is illegal even if all parties agree to it. Brokers of all kinds, historically, have put buyers and sellers together for a fee.