Gender is not an innate biological characteristic but is indeed a social construct. Look at how gender norms have varied so widely across time and place. Blue was once the color for girls, associated with the Virgin Mary, while pink was the color for boys, considered a bold color.
Were the social construct of gender to be abolished there would be no gender dysphoria and transgenderism because each human being would be free to express themselves as individuals without any "male" or "female" assignments to the way they act or dress or speak.
Transsexuality would still exist, but not transgenderism, were gender to be deconstructed (which would require undoing thousands of years of artificial social construction.)
Some aspects of gender are socially constructed, but gender roles are at least to some extent biological (see: testosterone and estrogen).
