Let me lead you step by step into why I disagree with you.
1). This is the link that you linked to.
Catholic veiling, the history of veiling in God's revelation. Jewish and Catholic history of veiling. Liturgical veiling, women veiling, & veiled prayer.
www.prayinglatin.com
2). It has has these words:
Veiling has been a part of sacred history from the beginning. God reveals Himself to His people through veiling, and He directs His people to approach and worship Him through veiling.
Veiling traditionally covers over things that are holy, mysterious, or beyond ordinary human comprehension. Veiling has also been associated with protecting that which has a particular holy significance or dignity.
Then it goes on with a long spiel about holy things: Tabernacle, Christ, altar, etc. being veiled.
Then it ends with its conclusion (comparing these other holy things and Christ with headcoverings for women):
A bride also veils herself before she gives herself to her husband in
holy matrimony. Her veil represents her holy purity and thereto hidden nature. A woman’s body in particular is a sacred temple, like a tabernacle, in which new life is conceived and brought into the world, and God creates and unites each soul, which He knits together and forms in the womb of every mother (
Isa 49:5,
Jer 1:5). Just as we veil the life-giving tabernacle that contains the Bread of Life, likewise the life-giving woman bears and carries on the veiling tradition.
From the very onset of the Church in the first century, as St Paul himself attests, women always veiled in church, in the presence of God. Saint Linus, the second pope, in one of the only things we know of him, decreed that “all Christian women should veil their heads when inside a church” (Roman Breviary, Matins Sept 23,
1). Other Church Fathers such as
Tertullian and
Clement of Alexandria also attest to this apostolic tradition. A woman’s veil uniquely symbolizes her humility and relationally being cherished and protected (
1 Cor 11:3-16). Her veil is also a visible sign that a woman has become a living icon of the Church and is like the Church a bride of Christ with Christ as her Lord.
So the inference and logic is this:
altars, chalices, etc. are holy and veiled
Women are holy and therefore veiled.