I can't do much against such staunch and flat disagreement except keep on being wrong, but ah well. I understand the argument that as a self-insertion character in a third person game, he should be infinitely moldable to meet a player's requirements, but history doesn't really bear this out. You may disagree with the attribution of Link with anything approaching a personality and I can understand that, but the truth is that throughout these many years, he has remained largely unchanged. You believe a gender swap would be insignificant because he is an androgynous male, but an androgynous male is still a male.
Link may not be a well rounded and strongly defined character, but I don't think I (and others) arrived here by accident or chance. In the course of so many games, and in the face of increasing use of facial animation and other subtleties, Link has been instilled with limited but (for me) undeniable personality traits. To some degree, he has come alive, and has been doing so since at least Ocarina.