This is closely related to a failure mode of communication discussed here recently. The error made by the "fascists" and "rakes" in the linked post is a special case of the OP's error of assumed variables: in this case the hidden variable is whose morality applies.

My guess is that these miscommunications often arise from inadequate empathy or theory of mind. It's very common for assertions to have hidden or assumed variables that are reflexive, that is, they refer to the speaker. Some people have the ability to automatically transfer the hidden referent when changing such an assertion's subject, and others must to reminded to do so. (And indeed, in some cases some will argue that it's not appropriate to transfer the referent!)