The Fallacy of Denying the Inference

Consider the following conversation:

• Timothy: Hi there. I am not married, nor have I ever been married. 
• Bob: Oh, so you're a bachelor, eh?
• Timothy: I never said I was a bachelor. Why are you putting words in my mouth?

I've been encountering this line of reasoning a lot lately, and it drives me nuts. I was hoping to give it a silly or fancy name, but I think Denying the Inference seems pretty straightforward. It happens when people basically accuse you of straw-manning their claims, despite the fact that your description is a perfectly logical entailment from their original premises. It happens so much, in fact, that I am honestly amazed that no one has ever bothered to name this thing before (or maybe there is, and someone can just point it out for me?). 

My personal experience of this came recently when I had a discussion about formalism vs Platonism in mathematics. I tried to explain that formalism is basically the de-facto presumption in a number of modern textbooks, as evidenced by such phrases as "the language of natural numbers" or "the language of logic." We also see a lot of modern pedagogical sources that encourage educators to teach math "as a language," not to mention the existence of "formal language theory" as an actual class you can take in upper-division mathematics. The natural numbers themselves are nothing but a closed, tautological circle, as evidenced by the Peano axioms and the textbook definition of "zero." My detractor, however, rejected all of that entirely. Instead, he demanded that I produce an actual textbook containing the explicit affirmation that "formalism is true."

The obvious problem with this line of reasoning is that you don't have to explicitly affirm certain propositions in order for certain other premises to do it for you. When you tell me that Tim has never been married, it cannot possibly qualify as a straw-man argument for me to infer that Tim is a bachelor. Please don't blame others for your inability to grasp the logical implications of your own claims.