Speaking the truth straight out can feel good, but it is rarely a good rhetorical strategy. Instead, back up, and start with this: what do the people across the table want? What do they believe is good, and what do they believe is important?
Now, how do you recast your arguments to appeal to those goals? How do you frame your position in such a way that they will want to agree with you?
This is the foundation of convincing people: empathize, understand them, learn their communication patterns. Once you see how they communicate and think, you work down those routes but send the message you believe is important.