What's a phrase you hear a lot, but disagree with?
One that comes to mind for me: "Whatever doesn't kill you makes you stronger" is not always true. Maybe even only half the time!
Are there any phrases you tend to hear and shake your head at?
No, you asshole, we are getting to the bottom of this: you expose your reasoning for your position and I will do the same and this ends when reason doesn't support anymore one of the 2 sides.
Some things are truly just up to personal preference. "Agree to disagree" is a perfectly valid thing to say when discussing how to cook a steak in my opinion.
True. How to cook a steak, whether coffee or orange juice is better in the morning, are topics upon which reasonable people may differ, and for those, agreeing to disagree is a perfectly reasonable thing to do. However, an aggravating number of people genuinely believe that whether or not trans people should be allowed to exist is one such topic, and say this to avoid having their beliefs challenged.
Reason alone rarely if ever supports only one side or the other. You choose how you are weighting things; that's an emotional response, not a logical one.