Who is Flash's archnemesis? I mean, Superman has Lex Luthor and Batman has Joker, who's Flash's baddest of the bad amongst his rogues gallery?
Motivations / Reason / Code - Unlike the Reverse Flashes, Cold & company have independent motivations, can be reasoned with, and have a certain code of conduct. That means that when confronting Cold you can't just go full bore and attack all out every single time... you may be able to convince him to act otherwise or his reasons might even align with yours. That makes the situation more volatile and risky because their actions and motivations may be targeted at someone else or you might actually end up stopping them from doing something arguably good. The whole potential for reform is a big part of what made the Rogues distinct from other galleries. With the Reverse Flashes- who are all certifiable- you can simply go all out every time without ambiguity.
Negation - Captain Cold's gun saps kinetic energy which really means it's more a "slow gun" than an "ice gun" as generally assumed. He can stop bullets and, with planning, throw down fields to slow speedsters. This dynamic means that he can challenge the Flashes but only with planning and preparation (or luck), meaning that any encounter is one where Cold is figuratively one step ahead- with traps and contingencies in motion (otherwise he wouldn't come to play). Again, this is potentially more interesting than just showing up fighting with the exact same power set.
Organization - Cold is basically a super-powered mob boss which puts many other super-powers at his disposal. It is Cold that decides whether Mirror Master 'ports you out of Iron Heights not just any of the Rogues. While this may seem like "cheating" the mob structure is Snart's tool... just like Luthor wouldn't be as much of a threat without his money, power, influence, corporation, or scientific infrastructure. To discount Cold's organization would be like putting Luthor alone up against Supes in a fist fight. It's an integral aspect of what makes him a credible threat.
That doesn't necessarily make Captain Cold the archnemesis but, at least to me, at least more interesting.
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