Most likely from movies and other pop culture. Real radio code is intentionally stiff so movie screenwriters try and make it sound right but more friendly.
This probably originates from half duplex communication where the sending side indicates they are done sending by saying over. In the military, the ranking side is entitled to end the conversation by adding "out"
The article talks about it, how it never makes sense to say both because the phrases are redundant and contradictory. You would either say one or the other to indicate that you have finished speaking, your choice indicating if you intend to hear a response or not.
You don't say that, you either say "over" (I've finished talking, go ahead and talk more yourself) or you say "out" (I'm done talking on the radio now, bye).
I can only guess it was from Hollywood, but in the military no one uses it because it's wrong. People down vote for several reasons, but I don't worry about that usually, I'm just here to talk to others a bit and read about technology.