That's rather an argument against you having a feminine gender identity. Remember that gender is the social and cultural differences considered appropriate for one's sex in a given society.
Well, no. People have gotten too hung up on this "gender is a cultural phenomenon" canard, and failed to realize how incorrect it is as such gross oversimplifications typically are. Specifically people are conflating two related but separate phenomena, gender
identity and gender
expression.
Gender
expression is the cultural component, where society decides what appearances, roles, and behaviour patterns are "appropriate" or "desirable" for a given gender. This can vary widely from culture to culture, and is only partially based on biological differences or imperatives. When people say "gender is a social construct", what they are really talking about is expression, how that expression is stereotyped, and those stereotypes enforced by the particular culture they exist in.
Gender
identity, by contrast, is innate to the individual. It is the individual's internal body image, how the mental/neurological image of their own body matches up with their actual physical sex. In cis-gendered people there is no significant difference between their internal body image and their physical sex, so the concept of gender identity separate from physical sex is alien to them. However, in transpeople, there is a fundamental dichotomy between how the individual perceives themselves, and how their body is developed.
The body image/body type dichotomy is the origin of Gender Dysphoria Disorder (GDD), and there is a growing body of evidence that this is fixed at a very young age, prior to puberty. This is uninfluenced by cultural or other social influences, and does not seem to change at all from childhood to adulthood aside from the comparatively minor changes that accompany puberty.
Interestingly, as an aside, transgenderism is not the only conflict between internal body image and the actual physical body, there are a number of others, some of which appear to be developmental, and others the result of neurological trauma, some of which are permanent, some transitory; eg Body Integrity Identity Disorder, Alien Hand Syndrome, and Depersonalization Disorder.
Where the confusion comes in is when there is a the conflict between
identity and culturally-enforced
expression. In some people, their expression of their body image conflicts with cultural norms of "masculinity" and "femininity". This can be seen as an aggregating factor for GDD, which exacerbates the identity issues, but does not directly cause them. All societies have some concept of "masculine" and "feminine" expressions that vary widely both in their construction and their enforcement.
So we see biological females with culturally-defined "masculine" expressions and biological males with "feminine" expressions. When gender expressions for cis-gendered individuals do not match cultural norms, they are often stereotyped as expressions of homosexuality, and are often linked to homosexuality -- the stereotype of the "butch" lesbian and the "effeminate" gay man -- but are not exclusively tied to it, as we see with the existence of heterosexual "tomboy" females and "sensitive" males.
Further problems are caused when the cultural enforcement of such norms are based on a strict binary, when research increasingly indicates that gender identity exists on a spectrum between the two binary extremes.
So this combination of identity and cultural enforcement of expression can lead to confusion both in transgendered people, and non-conforming cis-gendered people, which can end up forcing people into a particular cultural pigeonhole, stereotyping them as gay or lesbian or some sort of deviant identity when they are simply non-conforming with regard to cultural norms. It's also possible that many of those stereotyped as "butch" lesbians or "effeminate" gay men may also be gender non-binary as well, but have not had the understanding of what that identity means.
Which brings up another factor contributing to identity confusion, the lack of referents. The individual lacks the necessary referents to understand the difference between their body image and their physical sex, and what that means for their identity, and how it affects their expression. This is particularly common for younger people in cultures or sub-cultures where expression and identity are strictly enforced, and the existence of non-conforming individuals is strictly repressed. Christian and Islamic fundamentalist cultures are the obvious examples here. (That is my own personal experience, growing up in a profoundly religious family and sub-culture.)
So this socially-created confusion between expression and identity is the reason why transgendered people, especially pre-adolescent children, are required by medical standards of practice to undergo extensive counseling and therapy before they can even be considered for transitioning their physical sex to match their internal body image. It is also the reason that many consider the recent upsurge in those identifying as some form of transgendered, binary or non-binary, to be simply trendy bandwagon-hopping. It is a "trend" only insofar as many more people now have the referents and information necessary to begin exploring their own identity and expression in ways that were repressed or prohibited in the past. It will take more time and more research in order to decouple identity from expression, lessen this confusion,1 and enable to people to achieve a better understanding of their own individual identities and expression.
One thing that continues to be a problem for many transgendered individuals is that the medical standard of care historically enforced a strictly binary view of gender identity in line with cultural norms of expression, and continues to do so to a slightly lessened extent. Hopefully, as research continues, this will be corrected as well, and a greater understanding and acceptance of the range of gender identity will result.