This has never been obvious to me, and I continue to be confused by it as a position. It seems similar to "don't respond to anyone making blatantly false/harmful claims on discussion forums, because engaging with them just encourages them and spreads their message". In fact, in the Twitter case, it's even _more_ nonsensical to me - because the audience in a forum is general (and so, is likely to contain folks who are "on the fence" or who agree with the troll), but your Twitter followers are, by definition, those who hold similar opinions to you (and so, are likely to agree with your "takedown").
I'm not saying that you're wrong (I've seen enough apparently-smart people espousing this opinion to convince me that I'm the one missing something), I'm saying that I don't understand it. Can you help me understand what I'm missing?