Even further, not everything is a math proof, where everything has been standardized and open (although understanding the proof is a whole other topic). Heck, take it one step lower - coding - and even though theoretically the source code is 100% transparent, still often times your claims are not reproducible because of environment. Now lower it one more to any kind of science where replication is expensive and/or hard, and then one step lower to personal experiences... And yeah, things can seem tough, can't it?

And even in the case of mathematics proofs, that tells you nothing about things such as: extendability, taste, where future direction should go, what this philosophically means, etc. Which we definitely do care about.

It's funny because the people throwing around fallacy accusations everywhere don't understand that they are semi selectively using fallacies alongside claiming universality while not actually practicing it (not that you have to, of course, I very much don't agree with that premise, but if you're the one saying it...)

Anyways. /rant, it's crazy how many people don't discuss these basic but subtle ideas. To be fair, I struggled with the same exact things when I was 15, and it doesn't seem like you get taught this kind of nuance until maybe the tail end of a rigorous bachelor's degree, though personally I only learned this stuff on my own through extensive trial and error and suffering.