As a business analyst, one of your roles is to help the client make good decisions.
There are times when you will determine that the right course of action does not match what the client is understanding.
Your role is to help the client understand the reasoning for the course of action so that the client can make an informed decision. Sometimes this puts you in an uncomfortable position.
At these times, keep your focus on the value you can create for the client. If you let the discomfort control you, then the client will either miss out on value or lose value due to a poor decision.
Stand your ground and clearly outline what the situation is and what the results of the different courses of action are. Being uncomfortable in these positions is part of the job.