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I wish there was better etymology on verb phrases in dictionaries.
For instance, put seems to come from a word meaning push. Out means away from the focus. It makes sense to me that while put out has many usages, they generally mean to shove away, to defeat or disappoint,
When you outen the light, some people say that’s putting it out. Firemen put out a burning building. The vet put out the dog in order to “fix” what wasn’t broken. We put out The Observer every Wednesday, no matter how little news we had. Rocky Colavito was put out when he tried to stretch a double into a triple. My wife was put out when, without warning, I had to work late. He read the blueprints wrong, which put the window frame out. He asked her to dance the hokey pokey with him, but she didn’t want to put her left foot out, having put out her back hoisting a canner of tomatoes. Put out the word: choir practice will be on Thursday instead of Friday. Put out the cat. Lieutenant Commander William De Vriess put the Caine out to sea. Put out the bottles for the milkman. Put out the leftovers on the buffet. Put out the laundry on the line.
But when Susie gets randy and puts out, she isn’t pushing away but drawing closer, not expelling but inserting, not extinguishing passions but arousing them. It’s just the opposite of what I should have predicted; we don’t talk of a flame putting out a moth. She’s not being inconvenienced, she’s being indulged. So where did this “put out” get the opposite sense?
In the words of Yakov Smirnoff, “Whot a language!”
I think you are looking at it backwards. Rather than the physical drawing closer or inserting, this means that the woman is extending favors. Giving herself.
On rare occasions I have heard this meaning of put out used in different contexts. Usually getting money from a source when it was not easy to obtain. “The bank finally put out and gave me the loan.” “I played the slot machine for two hours before it finally put out.”