There is another theory that says Neo and Smith (opposites) cancelled each other out when Smith took over Neo, and this is the sole reason Smith was defeated. While this is "mathematically beautiful" to think about (and it is an additional layer the Wachowskis very likely thought of), it just doesn't make as much sense when thought of as the only plot device to explain Smith's defeat. I don't think there is some mysterious, inevitable disintegration that must happen when opposites join. We saw Neo's body being used as a channel through which Smith was destroyed. It seems this was action proactively taken by Deus Ex Machina.
I also think Smith would have been smart enough to know that such a thing would happen if cancellation alone could destroy him, being the ultimate computer virus that is able to think and make decisions to ensure its own survival (and also having taken over every other program in the Matrix, including the Prime Program, the Oracle!). Oracle-Smith definitely would have forseen such a predictable way to die. But not even Oracle-Smith could forsee his own death when it is caused by Neo's non-understood decision to give himself up (see Smith: Smith's Defeat). Not only that, but if the Oracle knew Smith is Neo's opposite, certainly Smith would know too since he copied over the Oracle.
I've seen the argument made that Smith had no choice when it came to taking over Neo at the end of M3: even though Smith didn't want to, he had no ability to deny his purpose of destroying the ultimate anomaly, the One. Under this argument, it seems feasible at first that "opposites cancelled". But this doesn't seem consistent at all with how Smith behaves.
For example, just before Neo and Smith engage in the Burly Brawl in M2, Smith can't wait to copy over Neo. He isn't exactly saying, "Oh no, if I copy over you, it will cause us to become mathematically null, but alas I cannot deny the impulse!" No, Smith has no clue that taking over Neo could destroy him. Smith is practically foaming at the mouth in anticipation of copying over Neo. "...we're here to take from you what you tried to take from us. Purpose."
I would guess that the Wachowski brothers thought of cancelling opposites in more symbolic terms, as a kind of imagery running parallel to the actual plotline explanation.
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