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Aeolus451 said:

Argument from fallacy is the formal fallacy of analyzing an argument and inferring that, since it contains a fallacy, its conclusion must be false.

Trying to use "it's a fallacy" to dismiss other people's points or win in a argument  easily turns into snake eating it's own tail. 😹

If you're not bothering to break down why someone's logic or argument is unsound while you're using "it's a fallacy", it's just noise.

While it doesn't establish that the argument is false, it does indeed mean the argument in its current form is invalid and thus any conclusion drawn from said statement is at the very least dubious if not outright false. 

You're jumping into a weird position by countering in this manner by dealing with the distinction between the following:

"Argument contains a logical fallacy, therefore it's false."

"Argument contains a logical fallacy, therefore I am not accepting its inferences."

In the grand scheme of things, these differences are obsolete. The onus is on the claim maker to establish their conclusion. By failing to do so, whether or not the flawed argument's conclusion is true or false is entirely irrelevant. Garbage in, garbage out.