First, my standard observation that the term 'fallacy' is often misused. A fallacy, properly put, is a mistake in the structure of an argument that makes a claim invalid without considering the sense or meaning of the argument. You're actually asking about a rhetorical tactic: an effort to persuade someone (reasonably or unreasonably) of the 'truth' of a claim as a matter of semantics, not structure. Rhetorical tactics are a normal part of argumentation — the only reason we make arguments is to convince others of senses and meanings — but note the irony that misusing the term fallacy is itself a bit of a rhetorical trick.
The particular thing you're talking about might be covered by a number of 'informal' fallacies (what I've called 'rhetorical tactics'): begging the question, questionable causal chains, appeal to popular thinking, false equivalence, hasty generalization, or others as yet unspecified. The list of informal fallacies grows and changes over time as people grapple with different kinds of rhetorical ploys.
If you want a general category for this kind of tactic, though, I'd call it argument by implication. The aim of this kind of rhetoric is to imply a reasoning chain without expressing it. Obviously we can't condemn implication, because it's an essential part of logic and reasoning. I'd go so far as to argue that we get the term 'fallacy' (in its proper sense) because the Ancient Greeks laid out the basic forms of simple implication — the extension of properties from categories to their members — and noted which forms were valid and which invalid. But pernicious implication is common enough, and generally falls into a few different types:
- Invoking bias: conforming to listeners' biases, so that they will accept a conclusion without needing to hear the reasoning explained
- Weaponizing ambiguity: using vague pointing to force opponents to do all of the cognitive work, since the opponent must lay out the implied reasoning before s'he can critique it
- Deflecting accountability: attributing unexpressed arguments to vague or absent others, who are implicitly assumed to have plausible justifications
In short, pernicious implication uses natural forms of cognitive laziness — the preference for mental shortcuts and the resistance to heavy cognitive work that all of us are inclined towards — to get listeners to mislead themselves.
Of course, be aware of the opposite side of this coin — argumentative dissection — in which someone refuses to accept any form of implication, and demands proof or evidence for even the most trivial extensions of reasoning. Sometimes these are even used in tandem, where someone makes vague, general statements and then demands that others prove them wrong according to impossible standards. There is a cautious balance: one should say enough to make an argument clear, but not get caught in the trap of over-explaining.
The best approach I've found to dealing with people who use pernicious implication is to feign (or actually practice) open-minded ignorance. Tell them you don't follow their point and ask them to explain; pester them with questions to draw out the unexpressed reasoning; challenge their egos with little jabs like "Seriously? That's the best explanation you can give?". The goal is to force them out of that fortress of cognitive laziness onto the open field of expressed ideas where (more likely than not) they have few skills; people with real argumentation skill rarely hide behind implication.