Cortana in Halo is different from other AI in the Halo universe. She's a clone of Dr Halsey in mechanical form. Halsey is vain, but at the time she creates Cortana she was already old and one of the things she was vain about, her looks, had already deteriorated due to age. Since Cortana is a clone of Halsey she is also vain and prideful, and also angry because she is clone and an ai which means she doesn't get to live a long life. Cortana makes herself look like a young naked version of Halsey because its the only way she can get back at Halsey.