Usually the primary reason is piracy prevention, by requiring a game to always be online it’s hard to play/use a pirated copy. (And/or do “light” piracy by letting your friend borrow + install your legitimate copy.)
A secondary reason is to prevent cheating on achievements and the like. “Cheating prevention” is also often in play when there is some kind of monetization ingame, to prevent you from using a console command or similar to just give yourself the buyable items.
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