Examine word "reverse" in the dictionary.
reverse as a verb: means to move backward
as an adjective: going in or turning around to go in a direction completely opposite the one you were just traveling in.
as a noun: the opposite or contrary to that previously stated.
In this sentence, reverse is being used as a noun.
So, take the first part of the sentence before the semi-colon.
- The initiating kissing (for whatever the reason), is the man.
after the semicolon:
Ans: Men don't respond with kissing if a woman initiates romance. [It's the reverse]
Now, just add "more often" - it just happens more often that women respond to sexual advances with kissing vs. when a woman initiates romance, men respond by kissing as a response to her advance less often.