As a designer, our role is to convey the message using the most suitable medium. Medium may not be perfect, but it at least eases the task of end user to perceive the message. And as a designer though our prime focus is on end user, skipping needs and greeds of stakeholders may bring havoc. So how do you handle those situations wherein what you anticipated, rather inferred from research and user studies doesn't sound good to stakeholders. They don't see the value and you are sure that it is the correct way.
You have to persuade them. Either being nice and polite or strict showing consequences. And what type of consequences? You might think of terminating the project and vowing not to work with such clients anymore. But take a pause and think where the problem is. Most of the time its communication gap. They assume that you'll assume the same thing they assumed ! Stumped.
But literally they always think that the product is going to take the form they have assumed cause, they have been talking to you. As a designer you should have the skills and capability of taking out the unsaid from the mind of your stakeholders/users. They can't perceive or see what you can and its true vice versa too.
So based on my experience, I would say be persuasive in nature. Provide enough evidence. Statistics might not make sense but a story would. And this soft skill will not only help your professional life, but a personal one too.