Ditto JR. Let me add that "ways out" here is essentially literal and not a figure of speech or idiom.
A "way" is a path or method. "This is the way we fill out time sheets here." "Do you know the way to San Jose?"
"Out" of course means the opposite of "in", not within the border or heading to a place not within the border. "I am going out this door."
So a "way out" is a method of getting outside the border, i.e. an exit or escape. "The only way out of this room is through that door." "The only way out of this sales slump is with a whole new marketing strategy."
In this case, the writer is saying that the proper "way out" of a romantic relationship is a face-to-face conversation, as opposed to sending a text message saying "sorry we're through i just met someone prettier than you".