I can walk outside and prove gravity.
I can find a million pictures of the earth taken from space, look at a globe and view trade routes that circumnavigate it. I can also look to the sky and see the sun and moon are clearly circular which makes a pretty good case for a pattern.
Climate change or the age of the earth are based on a whole lot more interconnected bits of science that even if you studied your entire life you could not truly say that you understand. You’re putting your trust in layers of science that add up to a certain conclusion (which is good). When people are given good reasons to believe that science and peer reviews aren’t always legitimate it undermines that process of trust building on trust.
Modern aviation is layer upon layer of science building on each other, but I can easily watch a plane takeoff to validate all of those processes.
That’s it in a nutshell. If you can easily replicate it, it’s easy to trust. If you can’t, it’s not…especially when it’s used to drive politics.