Has any name been assigned for a class of informal fallacy (or cognitive bias) in which someone shifts in dialog between use of various premises to support an argument, without ever allowing any to be adequately examined?
For example, consider the following hypothetical exchange:
Speaker A: Hypothesis H is supported by premises P1 and P2, either of which would be sufficient independently.
Speaker B: Support for P1 is rather weak at best.
Speaker A: H is still supported by P2.
Speaker B: Have you considered common objections to P2?
Speaker A: No, but they would be irrelevant, because no one ever refuted P1.
(Also, is any source available giving a recommendation for how to confront use of this fallacy for an audience or speaker who may not otherwise recognize it?)