Here are some of the possibilities:
1. Souls have genders and their soul-gender and body-gender didn't match.
2. They lived many past lives as male or female and weren't used to being male or female.
3. They planned a life as male or female and accidentally entered the wrong body by mistake, in haste, or without thinking it through.
I believe that any answer would work for this question as it would for questions regarding any other condition in life. Why are people born without limbs? Why are people born with extra limbs? Why are people born in poor circumstances in which they have little or no opportunity? Why indeed! I think that people choose certain circumstances for each their own reason, even though the reason becomes hidden to them during life. I further believe that reasons we conceive of while living on this earth cannot come close to touching the reasons we actually consider while on the other side.
I think that if we were to discuss this in terms of personality, rather than culture or physical sex, it's a bit easier to discuss and understand.
Some say that as souls, we exist in some sort of neutral state. I myself, I don't agree with that. I think that you are who you are and this exists within the soul as a "base" energy level and this is what is transferred into your body and it's what we call "personality".
And technically, all personality is, is a point on a spectrum. And in fact, points on many spectrums. And sometimes, what our personality is, may not always line up with your physical bodies and this creates an issue because of cultural expectations.
Having been as lucky as I have been to have the volume of research that I have been able to do I've come to two main conclusions about reincarnation.
1. We chose our body and present life for a reason.
I think that in accepting this fact, we can come to peace with our inner selves and those around us and in our families.
I think that it becomes too easy to scapegoat god, the universe or something for our choice, especially when we face difficulties in life. And all that does is create noise and static that prevents us from learning the lessons meant for us in this life and from being able to hear and see the subtle hints and nudges that are meant to guide us through life.
2. We all have a "purpose point" in life.
After we are born, we have to play "catch up" for a bit and relearn how to navigate a world that has changed while we have been away.
But we all have a point we will all eventually reach where everything just sort of "clicks" and comes together. This isn't some over romanticized moment of predestination, but just a simple point where you can begin to look back at your life and start to see a long chain of connections forming. Say perhaps if you hadn't X, you never would have Y and met Z. Those kinds of things.
And it's also at this point that you begin to move forward in your spiritual growth and also in you current life. But that point is also flexible. If we can't get the hang of #1, reaching the "purpose point" can be delayed, moved and even not achieved in your current life.
There are many attempts that go on behind the scenes to reschedule this point because in spite of what people may think at times, "the other side" wants to see us succeed and actively help us to do so. And the key to life is truly "it's not what happened, but how you handled it".
There are so many different people, situations and life plans out there, I want to avoid getting into specifics and I'm only qualified to speak on behalf of myself anyway..
But I struggled with gender identity my whole life. I can't say it anymore simply than my base personality or energy is female. I went through every explanation and option out there and none of them fit. And then one day I was sort of shoved face first into reincarnation and after a few years, it all made sense.
I was past my personal purpose point before I had discovered reincarnation and it had helped me see that the choices I had made were the right ones. If I hadn't made them, none of what I have now would have been possible. My former sister in law is now my wife, my former brother is now my son ect.
I really began to put some deep thought into it and then it struck me; I choose to be male. How else could I have married my sister in law (who stayed female) and then had my son (who also stayed male)?
And then I had my second question, why would I do that? Why didn't I (or we) arrange it so I could have been female again? The answer to me was immediately obvious: because I'm here to help them. And knowing me, that's exactly the sort of helping, supportive and selfless decision I would make.
There's lots of other little lessons I'm learning by being male too, but I won't get into those here. But having all of the research I've been able to do and through my own intuition, I can see how it happened before and how that translates into the issues I am dealing with in this life.
And so in summary, you (or anyone) just has to have faith that even if you don't know what it is, you have to feel secure in knowing that there is something laid out for you and that there are people and resources available to you to help you along the way.
But you also have to love yourself enough to give yourself the opportunity to see the path that is meant for you. I once told someone that just because you've never had something before, is no reason to think that you won't get it.
You can only control you and that starts by learning to accept that you chose the life that you have now. Even if that's a stretch, you still have to accept what's on your spiritual/emotional/incarnate plate at the moment.
The ones that don't are the excuse makers, the blame placers, the finger pointers and the people that flounder rather than succeeding through life.
Regardless of the circumstances of our birth, we all have the power of choice.