I was in one of these awful, awful relationships. I no longer care so much about the precise definition of him, but the descriptions of people with Narcissistic Personality Disorder and Psychopaths (dramatic word, I know) fit it absolutely.
Cycle: Idealise/Devalue/Discard. They adore you! You are wonderful! You are their everything! You're wrong! You're ugly! You're so demanding! You're so clingy! They don't do drama! Goodbye!
Then some time passes and your phone rings...
"Oh hi, there, person I dumped like a bag of rubbish! Yeah, just wondering how you are. Maybe we could meet. I am having such a hard time with [insert excuse for calling] and I need someone to talk to... "
They were wrong, they're sorry, how about a hug, how about a little lie down, down about, er...
Because they adore you! You are wonderful! No - wait - you're too clingy. You are causing them so much stress! They are out of here! Have a nice life and goodbye forever! Or rather, till the next time they feel horny and lonely and bored and no one else is entertaining them enough.
It's referred to as "hoovering". Every time you take them back they get a little bit nastier. Mine ended up with a moment when I thought he was going to kill us both.
No Contact. It hurts and hurts and hurts and hurts. But really. No Contact.
Not to show they how you feel, not to teach them a lesson, not to intrigue them into coming back. But to preserve your sanity and your physical well-being.
PS. If ever you are in a relationship where you are saying/thinking, "At least this person never actually hit me," or "At least it's better than being alone," - get out. Please. Run.