- To learn is to gain more knowledge.
- Having more knowledge means having more that one can forget.
- ∴, the more one learns, the more one forgets.
First of all it's a non-sequitur (like all fallacies...), in the sense that "can forget" does not means "do forget". So just because you've got more to lose doesn't mean you actually lose it.
On top of that it's a purely qualitative argument, but what matters is the quantity. So is the increase bigger or smaller than the loss, at what timescales do loss and increase of knowledge happen. Are the rates fixed or relative. So is it plus X information (learning) and - Y information (forgetting) or is it +X information (learning and -Y% of the total information (forgetting). In the first case you could have a net increase in the second case there's likely some sort of dynamic equilibrium somewhere. Though you might never reach this dynamic equilibrium in your lifetime and so would still be increasing your knowledge rather than losing information.
Also what's your goal to begin with? Like say you want to stay above a baseline level between 0 and maximum knowledge, then not learning isn't going to get you there, so even if it's sisyphos work to learn and forget, you're still accomplishing something with it, so it's not pointless.
Though after all, unless we figure out a way how to avoid that, you'll ultimately die so all your memories will be lost like teardrops in rain and all you've ever known will be forgot. So the argument is kinda true, the more you learn the more you will forget. But that's not what matters to people, is it?