The fact that not everyone feels comfortable with the sexual identity assigned by God is neither here nor there. Many of us are not especially pleased with the way God made us. If we were in charge, we would make ourselves more gifted athletically or academically or musically, more charming, taller and thinner, and so on. Moreover, sex and gender are at least as fallen as anything else about human beings. Most of us have a hard time living with a wide range of sinful tendencies and have to struggle against the inclination toward sexual perversions, or alcoholism, or depression, or procrastination and laziness, or violent rages.
Sexual nature is by no means a special case.
Presumably, he did not choose them because men are better than women. One of the Twelve was his betrayer, a fact which Jesus knew well in advance. Moreover, no human can ever be as perfectly good as the Blessed Virgin. Mary is honored as the Queen of Heaven, Queen of Angels, Queen of Saints, etc. She is the Queen over and not the Queen among the Apostles.