Because one of the main arguments the modernist trads use to wear a headcovering is because they claim the woman is sacred. That’s why I care. Because it is factually incorrect. Yes, there are sacred men and women. They have been consecrated by the Holy Spirit through the ministry of the Church. You know them as clergy, religious men and religious women, male and female vowed members of secular institutes, professed diocesan hermits/hermitesses, and sacred virgin members of the Order of Virgins. They are factually sacred. But laywomen who want to wear a veil because they point to something that is special - the tabernacle, the altar, etc., they want to arrogate sacrality to themselves when there are people who actually are sacred.
If a woman wants to wear a headcovering because she wants to do something “traditional” fine. If she wants to claim that women are obliged, then NOT fine, because it is no longer obligatory. If she wants to wear a headcovering because she thinks its chic or because it reminds her of First Commiunicant innocense or because her grandmother did or whatever, fine. If she wants to do so because she thinks it is a virtue, not fine. So, the act itself is indifferent. But the motivation and the rationale behind it is going to be okay or not okay depending on what it is.
And let’s be serious here. A truly traditional woman would sit apart from her male family members because separation of the sexes at Church was the traditional practice. So modernist traditionalists are in fact cherry pickers.