In sociology, gender is social and sex is biological. Now that we have that fact out of the way, we can acknowledge that gender is basically an abstract set of ideas pertaining to sex. Some cultures even have more than two genders. The Navajos have four.
HOWEVER, even though some of those ideas have nothing at all to do with biology (liking pink or blue, for example) and a culture can have more than two genders, what came to be considered masculine or feminine didn't poof out of thin air. Stereotypes developed based on real, observable patterns in behavioral differences. At this time, with the help of MRI technology and other technologies, we know that on average, male and female brains have significant differences. Intriguingly, the brains of pre-treatment transgender people have more androgynous characteristics than those of the general population.
Transgender people are an excellent way to study hormonally-based differences. Female-to-male transsexuals who take testosterone experience reductions in verbal fluency which can be validated not only with verbal tests, but with MRI scans. I am not making this up and have personally experienced it, myself. Here is a link to the results of a fascinating study: https:// www.sciencedaily.com/releases /2015/08/150831001124. Htm
And just because gender is made up, doesn't mean its a bad thing. Many things that are great in our lives are made up. Like good stories, theories of physics, traditions, ...
What most people seem to mix up, is that gender is a choice, sex is not. So let people choose their gender, and allow people to keep their sex a private issue if they want to.
It doesn't help though that sex and gender use the same words to mean different things. If someone says "I'm female.", then they could mean, "I was born a female." or "I feel and behave female.", which can understandably be a source of irritation for some to whom this distinction matters. Say, a man wanting to father a child.
In the end, this should lead to most people to just ignore this whole matter of gender/sex, and just say - "I don't care if you call yourself male or female, and whether its your gender or sex." And once we're all there, we'll have gotten rid of sex-discrimination, which I believe is the root cause of this mess.
Standards for masculinity and femininity are made up by society, although influenced in part by biology. For instance in practically every culture it is more traditional for men to be warriors and hunters because of physiology, although some of these cultures both in the developed world, developing world, and even remote tribes will allow women to be warriors and hunters even if it's considered unusual.
But there's a completely different way "gender" is made up by society. Originally it was only ever used in the sense of grammatical gender, then for a long period of time it was used as a synonym for sex. Now it's meaning is changing because sociologists have decided to use "gender" itself to refer to the cultural concepts of masculinity and femininity rather than make up a new term like "gender expression-related identity", which they could have done considering that "third genders" exist in cultures that don't speak english as their first language and so we could've easily translated the category words for things like "fa'afafine" into "gender expression-related identity" rather than "gender" itself.
And finally another social force is effecting gender's meaning, people insisting that their "gender" is "male", "female", "bigender", "agender", etc... And basing it on a number of personal and subjective criteria. They may describe it as "I just feel like I'm really a [gender] on the inside" which is a vague explanation and may mean a lot of different things.
As long as you aren't hurting anybody else feel free to define your identity however you want. I will say this though don't bash people who want to define their "gender" in the sense of what parts you have or your chromosomes. I don't just mean all cisgender people. There are quite a lot of cisgender people I'm not referring to here.
I mean for example I think of myself as a "man" and I base this solely on I have male parts and XY chromosomes. I honestly don't feel "male" it's not something that feels like a deep part of myself or my identity, just a simple fact. I prefer to call myself "male" because as I grew up I understood the word to simply mean "A person with male parts". I find this understanding of gender to be short and simple and suitable for myself. Although I've never except during my self-conscious years in adolescence cared about "Being a real man" or tried to live up to standards of "manliness" I still call myself a "man" based on what parts I have, because it's easy and because my mind has better things to do than ponder what it means to be a "man". I am first and foremost an individual and I make decisions based on what I want to do, not based on living up to the socially constructed meanings other people attach to labels.
The first impression I have of this question is that you are saying gender doesn't exist- it is a concept invented ("made up") by society. I disagree with this because I believe, no, I know that gender is neither created nor affected by society. It is true that society has invented gender stereotypes, for example women who are practically physically flawless and nearly stick thin, and men who are super attractive and "manly". Society has attempted to redefine what gender implies, but gender itself is not created by society.
As society today has gradually introduced the idea that our gender defines who we are, more and more people are succumbing to the idea that, because of their personality, they were born the wrong gender. This is a matter of causing people to become lost in a search for identity in the wrong place. There are many new terms, such as genderfluid and transgender (one who has attempted to change their gender), to describe a person who has tried to find their identity in a different gender, when really personality is not affected by gender but by external influences- for example, what society tells us.
But gender exists separate to society, and is not invented by it.
If I have misunderstood the question, I apologise, but I'm afraid it is rather poorly worded and this was the best I could do with it.
This way of thinking would result in infinite genders. If you think that society made up 'gender' and only sex is biological it leaves gender to how people feel. This leaves unlimited possibilities, you can identify as another animal, an inanimate object, etc. Gender is more the behavior you express as a result of your chromosomes, and they hormones released, so gender isn't how you feel, it is how your body works.
So, I think I know what you are talking about. Gender, according to medical practitioners, the the awareness of yourself as male or female. But Gender itself isn't just "made up" by society, or as the left would say, "A social construct." It's actually both a mixture of biology and social norms that make gender for what it is, a subjective awareness of ones' sexuality. Males can behave more feminine that most boys, but the majority of males---across every culture---exhibit a range of similar "masculine" behaviors such as aggression, leadership, protecting their families, putting themselves in harms' way, and taking risks. Why? Unfortunately, testosterone isn't a social construct, and it quite literally sets the stage for a range of "masculine" behaviors.
Think of my examples like a cake. If I were to say, "show me where the egg is in the cake. Now show me where the salt is in the cake." Can you do it? No. It's all mixed. The same with gender. It's a mixture of both social norms and biological functionality.
If you are speaking scientifically and biologically -- No, gender is defined by nature; while science is used to explain the workings of nature.
But in order to properly respond, the question must define context. Are we speaking biology and science or are we speaking tumblarisms and SJW nonsense?
Proper definition is required.
Gender roles and gender norms are created by society, but gender itself is not. Gender is part of your identity. Studies have shown that your gender identity solidifies between ages 3-5, something which occurs within the mind of the child. Research has also shown that there are differences between not only the brains of men and women, but also in the brains of transgender and non-binary people. The studies of the brains of transgender people found that a transgender persons brain more closely resembles that of their gender identity than their assigned sex at birth. Thus a person who was assigned male at birth but who identifies as a woman has a brain that resembles a female brain, not a male brain. This is evidence for the reality of gender identity that has nothing to do with societal definitions of masculinity or femininity.
There is an aspect that is biological and an aspect that is cultural. It is obvious that men and women have different brains. We are a sexually dimorphic species who evolved to do different things. Men are naturally more aggressive and protective and women are naturally more nurturing. But still some parts are cultural.