I totally agree with what you say, "being born again" referring to reincarnation.
Throughout antiquity, belief in reincarnation was routinely accepted. Among many others, Pythagoras believed in it.
Opihikaobob, you may find the Christianity Support Forum a more welcoming place to post. Debate Forums seem to attract people who like to "take a piece out of you."
There are no rules about what you like to name your belief system.
Salute, agnostic Christian friend.
You said Aloha. Maybe you're lucky enough to live in Hawaii. Enjoy!