It's no more a bias than is the equally common mistake of believing that if "if A then B" is given, then knowing B allows us to deductively conclude A.

I think the term bias should be reserved for heuristics and cognitive optimizations which exist for very good evolutionary reasons but often go horribly awry, as opposed to things like "affirming the consequent" or the sloppy thought process you mentioned, which are symptomatic of an absent cognitive skill that we never had good reason to develop. The bias exploits a heavily selected-for cognitive process, whereas common logical ignorance is just a function of logical skill not really being part of our evolutionary heritage.