Now, if you know who made this argument, you know that it was intended neither to seek the truth nor to avoid error. It was, in fact, not really an argument, but instead a performance intended to elicit anger and draw attention. But, let's treat it as an argument, and see where it goes wrong, and how fixing the logic would get us closer to truth and/or away from error.
The most obvious problem with this argument, among the many that exist, is the lack of a connection between homophony -- the sound-alike between "Bane" and "Bain" -- and symbolic representation. Just because two words sound the same doesn't mean that one stands for the other. "Doe" and "dough" sound the same, but bread doesn't represent deer. Similarly, "knight" and "night" sound the same, but an armoured man doesn't stand for the moon and the stars.
At least, they don't obviously represent those things. You could do a little work here and establish a symbolic connection between the homophones. In the knight/night case, one could draw attention to the fact that knights were prevalent in the Dark Ages. The Dark Ages were metaphorically dark, in the sense that much learning and civilization was lost. At night, learning and civilization may also be lost, as those who prey on others -- indulging their bestial natures, so to speak -- are more prevalent at night. So, knight represents night because: knight connects to Dark Ages, connects to lack of civilization, connects to muggers and other miscreants, connects to the night.
Sure, it's tenuous, but metaphor often is. The point here is that what I've done is show how a little bit of logical analysis can make a bad argument into a better one. What we started with was an argument with an obvious oversight: there is no reason to think that Bane and Bain, despite being homophones, actually have any other relationship. What I've shown is that homophones can be made to have a symbolic connection, however weak, if there is a chain of ideas spelled out which shows a sequence of commonalities from one to the other. In the Bane/Bain case, one could say as follows. Bane the character is anarchic and destructive, desiring to destroy the things which make Gotham City worth living in. Bain Capital, according to some, was destructive and anarchic, acting to destroy things -- stable jobs, for example -- which make the United States worth living in. So: Bane is anarchic and destructive, Bain Capital is anarchic and destructive, hence Bane stands for Bain.
Of course, there are other problems with the argument. Batman, who opposes Bane, is a wealthy industrialist, which makes him much more like Mitt Romney than Bane who, in comic book canon, grew up in a Caribbean prison, before becoming the subject of macabre medical experiments. Furthermore, the histories of naming Bane and Bain are highly divergent. Bane gets his name from the word "bane", meaning a cause of death; Bain is named for founder of its predecessor company, management consultant Bill Bain. But, at least one egregious error in the argument can be corrected by examining the argument, noting its oversight, and repairing the oversight by making explicit a connection between the ideas.
Okay, so, that example was easy. Here's a more complicated one, this time of a good argument which reaches the truth because it is logically sound.