Statistically speaking, women disproportionately file for divorce more than men do. But usually this is a leverage position situation. But sometimes it's simply the person who files is recorded, but the other partner might have actually ended the relationship.
The only trend I tend to see, from observation and experience, is the partner with the higher social "mate value" will probably tend to do the breaking up versus the being broken up with. Mate value, IMHO, is relative to options and many people with options tend to explore them. Generally speaking, I think you'll find the average girl will have more plentiful options than the average man, if only in such that every woman, at least in the modern world, unless under force or born in the wrong place, has absolute power over sex as a commodity.
Something to consider is most breakup are not mutual affairs. Often there can be one side with lingering feelings or needs a longer process to form an emotional separation. Sometimes a person seeking a "friendship" is really asking to be placed in a holding pattern for another chance. Sometimes a person offering a "friendship" is just looking for a socially acceptable way to not deal with any lingering feelings of guilt or avoid conflict or to attempt to maintain a positive social perception amongst their peers. Clearly it's not easy being on either sides of that fence. Most people don't enter the process looking to hurt the other person. Or to prolong their own pain.
If you move on with a "friendship", if you meet a new person, then that's another situation you have to explain. It's another hurdle to possible surmount in a new situation with a fresh start. Also "friends" that were former exes often can become sources of tension and problems. A lot of people cheat with their exes on their current mate. I suppose the advent of things like text messaging, social media and Facebook has accelerated some of the opportunity for this. My take on it is why subject a new person with potential to added tension? It's already hard enough to manage the basic structure of initial courtship without unneeded distraction.
In the end, there is a practical legal side too. Hanging around an ex might mean you end up doing it and then you get her pregnant. How is that going to work out for you then? Or maybe two people get together after a long while and you find out she's got something serious she didn't tell you about, and if she's confronted, her choice might be to get kicked out of the house and be labeled a whore or to simply say you raped her, even if you didn't. Or her drunk boyfriend can show up at your door and try to punch you out because your ex is still in love with you and he knows it. I just see very little incentive for most men to really associate with their exes from a legal standpoint. It is a minefield out there and most men are often in a disadvantaged position of initial social perception.
The few instances where I think "friendship" might be viable is if you grew up with someone. Or you worked together for a really long time in the same field or industry ( Fishing off the company pier though is a different hot mess to live with) Or if you share a child together, which I think is the most salient and likely reason why a "friendly" or "friendship" situation might be practical. If you have a kid with her, you are stuck with that person for life, partner or not, you might as well try to smell the roses there than smell the latrine in that situation.
My guess is if you broke up with her, then she wants friendship to simply stay in that holding pattern to see if you change your mind. This would be true if you have a much higher social mate value than most of the other men around her daily life.
Or if she broke up with you, then I would suspect she would likely want "friendship" and offer it as a means to secure not having to deal with a full confrontation and possibly to retain you as an asset for the future. ( i.e. attention, free labor, maybe casual sex, etc) If this is the case, often the person has downgraded your value from priority to option. Life is short, really short, I just see little long term merit personally in retaining a situation where you are optional.
The last thing is IMHO, from my perspective, most women say lots of things at lots of times. Personally I try not to take too much face value with it. She might want to be friend today, but that might not be true tomorrow. Look at her life. Look how she interacts with people. Look how she deals with coworkers or friends or associates or men in her past. What does it tell you? What does it not tell you? If you determine that she isn't a great friend to people already in her life, what makes you think she will treat you any better? What most women say is one thing, but what most women actually do is what you have to really observe.
Sometimes it's not about how you feel. Whether that's how you feel about yourself or how you feel about her or who you felt about you together. Sometimes I think a person has to do what is best for their long term emotional health and personal situation. Just because you love someone doesn't mean it's the best course to have them in your day to day life. Sometimes the loving thing is to let someone go or give them a chance to start over without you or stay away from them because peace isn't possible.
Whether you left them or they left you behind, I don't see much point in following them. There's a reason why things end, and sometimes you have to shift from seeing it as a hindrance to seeing it as an opportunity.
