There’s a good number of reasons.
Tortured by Gravmind.
Rampancy.
Splitting her self apart to slow down the Didact.
Mabey even going into the domain corrupted her and made her mad with power.
Or all 4.
Interesting enough the Original Halo CE plot was to make cortana go mad with power and try to fire the ring.
Well that’s the thing.
The Encyclopedia on several occasions states that “unfortunately Cortana succumbed to rampancy before she entered the Domain”.
But that does run counter to how Halo 5 and Infinite depicts it. Surely if it’s Rampancy then it’s not really her choice to do all these bad things? Would the Chief be holding her to account for these things and consider that a betrayal of trust?
I think they wanted some drama and must have thought that if they told the audience “she’s rampant” people would just switch off and it would be less dramatic. You can’t do a redemption arc where Cortana admits she was wrong to Chief if you also say she was crazy because of an arbitrary event. You can’t create tension over a fear the Weapon will make the same choices as Cortana if you and the Chief should be fully aware she has seven years before we should be concerned.
From having talked to people on the Forums. Most people did leave Halo 5 with the impression Rampancy had nothing to do with it. Sure there’s people who say that doesn’t matter; she has to die. But the majority view seems to be she did it of her own choice and rampancy was a theory. So I was surprised they put that in since it’s at odds with how it’s depicted in Halo 5 and Infinite. The Chief doesn’t act like he thinks this is just rampancy.
Oh I knew about Halo CE original plot. But what I liked about Guardians was that she didn’t just go back and take a Halo ring; she went complete God mode and took over the entire Galaxy. That was really the twist in Halo 5. It was the sheer scale and megalomania of it. Plus the whole Rogue Servitor angle they went with was a neat idea to go with for a rampant version of Cortana; instead of just Skynet wanting to kill all Organics.
I think the Didact, who was recomposed in prometheans in “Halo Esclation”, take the apparence of the Warden Eternal and manipulate Cortana since the begining 
More seriously, even if Cortana have a lot of reason to became mad, that don’t changed the fact that everybody in the Halo Universe see her as the devil, that’s really sad for our well-loved AI. I would prefer the simple explanation than Cortana was controlled by someone eles or even fake, in this way her name would have been cleared