My random etymology guess here is one on one is from the origin of one vs one. One coming out ON top of the other. So one on one becoming simpler slang implying the same as versus.

Now one to one implies an equal relationship and especially in our field it feels weird imo to call them one to ones. Typical, you aren't equal levels in a 1:1 meeting. So maybe the one on one caught on because of the subtlety of one being on top of or above the other.

Face to face sounds too literal and agressive.

1:1 is an easy clear way to represent one on one. Although, we are forcing a double meaning on it. But hey that's the great thing about language. It's ever evolving.

Personally, in meeting titles I write PersonA/PersonB but I do type 1:1 over one on one when referring to the meeting type.