Looking for a word that fits "False Implication by Association"

Question

False Implication by Association (my term, maybe others as well.)

The concept is given from two sides of an argument the following;

Given that Side-1 believes NOT A. And, given that Side-2 believes A and also asserts B.

Then; there is an unspoken implication implied that Side-1 also asserts NOT B.

I know this is a false assumption, and a false implication, but the placement of the givens and stated assertion juxtaposed next to the Side-2 given, creates an implication/sense that there must be a counter assertion (NOT B) that is coupled to Side-1 (NOT A), even if unspoken.

I can only describe this as a False Implication by Association, but that doesn't feel right.

While I would like a single word, a phrase or any official definition or reference would be helpful.

EX:

Bob says: "I like Pepperoni Pizza."
Jan Says: "I don't like Pepperoni Pizza. And I have good taste."

This (falsely, and silently) implies that since Jan has good taste, and dislikes pepperoni pizza, Pepperoni Pizza must not taste good, and therefore Bob must not have good taste.

Answer 1

One important thing to note here is that no such implication exists. There is no suggestion whatsoever in Side-2 asserting B that Side-1 would assert NOT B (or indeed have any position on B at all).

Such an implication would have to come from an argument. The argument may be made by an actor mistakenly or on purpose. What you would call this depends on the apparent purpose of the actor.

If the false implication benefits an argument being made or position being defended by the actor, it is called a straw man argument. This term is used the describe a false representation of an opposing argument made in bad faith as an attempt to misrepresent the opposing argument and thereby discredit it or expose it to attacks which don't actually apply the the real argument. It may be an easy job asserting such a belief for Side-1 if sides 1 and 2 are generally opposed and if the idea that Side-1 asserts NOT B is popular, and making that assertion might benefit an actor, for example if attempting to criticize Side-1 for asserting NOT B. Arguments of this kind are called straw man arguments.

If the false implication doesn't benefit the actor, it's just a plain old mistake. As I said before, there is no rational connection between Side-1 and Side-2, so assuming that Side-1 believes exactly the opposite of Side-2 may simply be a mistake. This can happen if the actor drawing on such an errant implication is not very familiar with one or both sides. There's no name for it when it's not intentional, but I should reiterate here that no such implication actually exists.

Answer 2

You could say that Bob is reading too much into Jan's remarks. MW defines this as:

to think of (something, such as a comment or situation) as having a meaning or importance that does not seem likely or reasonable