"But it’s because the skeptic values reason as well, that they would have to have a justification to value their own freedom. They would have to have a non-arbitrary difference between their freedom and others’ freedom for them to justify valuing only their own."

By your own admission, it's not that it's impossible to value ones own freedom (which wouldn't even make sense because people clearly do that all the time), but that it would be arbitrary and thus irrational to do so, which brings us back to my question.

I think the thing here is that you believe extrinsic properties are irrational to value, but intrinsic ones are not, and I don't see a meaningful difference. Is this accurate?