Logic as Robin has most often used it is not "casual" it's the official meaning outside the technical mathematical forms. He uses it to argue philosophical points, not political opinions. It's the meaning that pertains to language, that can be expressed by a syllogism and violated by fallacies.
Using logic, as you just described it, requires carefully stating the premises, and then drawing conclusions. Robin often has not been doing that. People have challenged him to clearly state the premises being used, and he has evaded those challenges.
Challenging Robin to clearly state his premises is not snobbery. While some such arguments fail due to fallacious logic, the usual problem is the use of a faulty premise. Naturally, people want to be able to question his premises.