You come across as 'I'm right and you're wrong'. Even in cases where you're comfortable with your position, it's important to listen AND HEAR what the other person says. They may simply have a different perspective.
For example, in the case of the schools, if the star ratings were the only thing to be considered, there might not be much to discuss. But perhaps the other person is looking at the safety of the neighborhood, proximity, availability of extracurricularl activities, ability to socialize with a broad range of people, or any of about a zillion other factors.
Don't enter the discussion wondering how you can convince the other person you're right. Rather, approach it as an exploration - for both of you to get a chance to better understand the other and maybe seek out novel solutions.
Butting heads never works.