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You don't have to do this. Instead of memorizing fallicies, you can approximate the quality of nearly all arguments to two theory-of-truth claims:

1. The premises are themselves valid: you buy that they are truthful. 2. The argument's logic coheres: when added to your existing beliefs there is no contradiction.

Fallicies manifest through violations of these claims. But you don't have to know the name of that violation to raise a complaint: you can derive it on the spot. Discussing these fallicies mostly acts as a practice tool, and provides a useful bit of jargon if you are writing philosophy and need to convey the idea quickly. But most arguments in online spaces are dismissed with: "the premise is invalid" or "the reasoning is incoherent."