... in our homeschooling group. It seems to be coming up everywhere as it often does.

Fr. Z has a good take:

To be clear, I maintain that there is no longer any obligation under the Church’s law for this, but I think it is a good custom that recommends itself for various reasons.

Jimmy Akin provides this good entry regarding the old canon law (1917) and the new canon law (1983). It summarizes the case against it being a requirement.

Obviously the main sources FOR veiling are the following

1917 Canon Law, 1 Cor 11.

The main case against it being a requirement is 1983 Canon Law abrogating 1917 Canon law and a recent (relatively - 1976 IS recent in Church terms) authoritative CDF document with emphasis on that particular verse in 1 Cor.

Another objection [to a male-only priesthood] is based upon the transitory character that one claims to see today in some of the prescriptions of Saint Paul concerning women, and upon the difficulties that some aspects of his teaching raise in this regard. But it must be noted that these ordinances, probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance, such as the obligation imposed upon women to wear a veil on the head (1 Cor 11:2-6); such requirements no longer have a normative value. However, the Apostle's forbidding of women "to speak" in the assemblies (cf. 1 Cor 14:34-35; 1 Tim 2: 12) is of a different nature, and exegetes define its meaning in this way: Paul in no way opposes the right, which he elsewhere recognizes as possessed by women, to prophesy in the assembly (cf. 1 Cor 11:5); the prohibition solely concerns the official function of teaching in the Christian assembly. For Saint Paul this prescription is bound up with the divine plan of creation (cf. 1 Cor 11:7; Gen 2:18-24): it would be difficult to see in it the expression of a cultural fact [Inter insignores 4].(source)

Tempers fly with people insisting it is a current requirement for Catholic women to veil at mass. Others in the antagonistic fray claim it is a bad thing that should be prohibited. The two are not mutually exclusive. One can appreciate the practice all the while knowing that women are not damning their souls to hell when they don't veil. I think verbage like saying its prideful NOT to veil (because its biblical) is about as useful as saying that it is prideful TO veil (that whole self-righteousness, letting people see you while you pray bit) ... It usually gets there in due time. By then the discussion is out of control, neither side budges and everyone comes away hurt.

My opinion ... I think the case for the practice is quite good. I think the case for it being a requirement is next to impossible to hold. Why it can't be left at that is beyond me.