Conditional logic works just fine!

No, because in a social context, for people who understand implied intent and implied beliefs instead of just on-its-face logical propositions, it is an admission that the antecedent has a reasonable chance of being true. In social communication, if you don't believe something is possible, you simply dismiss any conditional statements following from it. Dispassionately arguing in a logical and objective manner is only possible for a tiny sliver of the population. The rest will get very angry and uncomfortable around such talk.