This is a perfect example. Even though you have worded this eloquently, your claim ("everyone is right, except in mathematics") is mutually exclusive to mine ("in some cases, two people speaking against each other cannot both be right"). Personally, I don't find your metaphor convincing. There are plenty of cases where not all parties are right.
We both used infinity haphazardly. You said both sides can't be right, I said all sides are right.
The truth is, it's even more grey than that. Sometimes both sides can't be right and sometimes some sides are not right. But the point stands, in reality you rarely if ever only have two sides and rarely if ever is any side demonstrably wrong in an objective way.
This isn't mathematics, this is the real world. Here issues aren't two-sided, they are dodecahedrons and all sides are right.