Vad har Takeshi kämpat mot, exakt?

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Spoiler svar:

Ultimately they are fighting against the de facto immortality that humanity has acquired, which is ultimately only really accessible to the extremely rich. Eternal life for the rich means eternal enslavement of the poor (I think that's a line from an advert for the show, even).

The human psyche is also not well-suited for such extraordinarily long lifespans. The Meths are really, really, really fucked up and basically all have god complexes; or at the very least they're really, really, bored after having experienced everything so often, and so will do crazy shit to have some fun and then throw huge sums of money at any problems that arise to make them go away. Also that the wealth inequality between the rich (Meths) and the poor (non-Meths, basically) absolutely dwarfs anything in present day society or before. Given arbitrarily long lifespans, the rich and powerful are able to accumulate arbitrarily large amounts of wealth and power.

The show doesn't usually scream these things in your face, though. Takeshi and the others don't usually sit there talking about exactly how these particular things are screwed up. But they're not hard to pick up if you pay attention and question them on your own.

That said, the leader of the rebellion, at least in the show, doesn't actually tell her followers that their true target is the elimination of immortality itself until she's just about ready to actually try to do that for real. In part because even rebels and poor people usually get to live an extra life, and can at least hold out hope for more. They won't truly be dead as long as their stack is intact, and that's a comfort. Nevertheless, they are fighting against the nature of society as a whole which is held together, at least in a military sense, by the Protectorate, and is embodied by the decadence and depredations of the Meths.