Well in a way you are correct, taito tríed to kill Kaito, in a way fails and Kaito kills him, and since I had this crazy idea of how Taito start existing, so what happened to Kaito in the end is that he, by killing taito, it was not only a defense act, since deep in his code there was a yandere part, waiting to be activated, and killing taito also mean to kill his love rival (since in this, both had a love interest on their master) so for that he activated that yandere part, activating that part of his code that maade him lose his Kaito self and start to be a taito instead... A little crazy idea, sorry 😅