I watched The Matrix Reloaded and I came away confused. In The Matrix, Agent Smith is this weird nihilist–he wants to scrub the matrix of free humans so he doesn’t have to be embodied any longer. When he complains about the sweat and the smell and the taste of humanity, he’s really complaining about the fact that he has to exist. In the world of The Matrix, the Agents are a security system that try to eliminate the free humans, and in a world without those free humans, Smith is free to shuffle off this mortal coil.
Killing Morpheus, Neo, and the others, then, is a very active nihilistic effort toward nonexistence for Agent Smith.
Then Reloaded comes along and Agent Smith is back again. At the end of The Matrix, Neo dives into Agent Smith and makes him explode. In Reloaded, Smith comes back, telling Neo that he “knew what he was supposed to do” and refused to do so. Because of some vague write/copy error, Agent Smith is no longer a security system in the matrix. Instead, he is a virus, and he’s real mad about something or other.
And that something or other is the weird, incongruous thing. Agent Smith’s was trying as hard as possible to hurtle toward death in The Matrix, but for some reason he stopped himself?
Even weirder is the speech he gives to Neo right before the “burly brawl” scene:
But, as you well know, appearances can be deceiving, which brings me back to the reason why we’re here. We’re not here because we’re free. We’re here because we’re not free. There is no escaping reason; no denying purpose. Because as we both know, without purpose, we would not exist.
[Several Agent Smith Clones walk in]
It is purpose that created us.
Purpose that connects us.
Purpose that pulls us.
That guides us.
That drives us.
It is purpose that defines us.
Purpose that binds us.
We are here because of you, Mr Anderson. We’re here to take from you what you tried to take from us.
[Attempts to copy himself into Neo]
Purpose.
A character whose entire being was formulated around a desire for death is angry because his purpose in life was taken away?
Ugh this movie y’all.
this cage is worms 
Yeah, but here you’re making the classic mistake of assuming that any Matrix movie after the original was supposed to have some function other than to make more money. If the structure and argument of the last two movies seems weird and sloppy and incongruous, it’s because they were afterthoughts.
I always figured Smith’s rejection of the rules of the Matrix in Reloaded was supposed to mirror Neo’s abilities being founded on his beliefs about reality. Smith is like Satan whining about humans and God, he’s complaining that Neo is getting special treatment by not having to die in part one so he too will reject the Matrix’s rules. And…that gives him copy pasta powers.
Then they tried to upgrade that into a causality discussion and predestination, which is a never good idea because it makes your character’s motivations inert, then they ditched all that in part 3 and made Neo into a magic christ man.
I dunno, you can almost see the footnotes in those movies that never really come together to make a coherent whole. Because everyone knows kung-fu.
I think you make a good point. The subsequent movies were trying to repurpose Smith as the antithesis to Neo. It kind of works, but it kind of doesn’t. While I would prefer Smith to represent an extreme embodiment nihilism, I think the simpler explanation is that he really just didn’t like humans, and he slowly becomes conflicted with anything that tries to limit his freedom (humans and machines).
They way you compare the Smith in the original film with the later Smith seems odd to me. I saw it as Smith being ‘broken’ by Neo so he should be different. At the end of the first film, Neo uses his newly found ‘powers’ to dive into and explode Smith which in that film appears to have destroyed him.
When Smith reappears later on he is changed or corrupted, no longer connected to the system in the same way. I assumed it was Neo’s fault, not really knowing his powers. Neo never kills anyone else in the same way as Smith maybe because now he knows better?
The new Smith is lost and broken, and focuses on Neo in a different way to the programmed determination of the original agents.
I’m not convinced that Smith wanted death, but instead to be free from the false-physicality of the Matrix, and so be able to go to either the abstract machine-mainframes, or perhaps into the physical machines of the Real World (the squiddies and so on). While from a human perspective, the desire to leave physical reality behind really really looks like a desire for death (because we don’t actually have any real experience of knowledge of a non-physical existence), from Smith’s perspective, he knows that there is a place where he doesn’t have to interact with these inadequate fleshy things, and can instead live the way he believes he is meant to, as a pure AI, because that’s where his orders (his purpose) comes from.
I can’t really speak to his behaviour in the sequels, because everything that comes after the original Matrix is weird. Take a look at the ending of the Revolutions game for one thing. So very very strange…