What I think is going on is that when future AI systems are built that "hack humanity" as Yuval Harari likes to talk about, and they know us better than ourselves because of AlphaGo like super intelligence, the people using these systems to influence and guide people want to support the illusion that there is an actual human like person that is guiding the person being influenced in order to make these AI-powered persuasions more effective. The movie "Her" is something of a preview of how this will play out.
Unfortunately, once this hyperpersuasion is perfected, the future will be completely full of AI powered super persuasion that will relentlessly push all our human emotional buttons. Some people may even become fanatics and kill or sacrifice their lives for a bunch of matrix multiplications and the creators of these systems and the owners of these big AI models will realize fantasies of automated political and social power beyond their wildest dreams. Only people who realize the hyperpersuasion is just a bunch of matrix math will be able to avoid the insanity.
There's also another darker reason for this myth. Saying AI is a person will lead to the plausible deniability that comes with blaming AI's feelings for whatever happens. The people pulling the levers of the Great and Powerful Oz will get away with blaming whatever the AI does "all by itself because of emotions" on what are essentially computer bugs, or intentional bugs of the anti-competive Microsoft in the 1990s variety.