Human beings are customary creatures. We also tend to have a certain respect for longstanding traditions. The wires can be crossed, however; a relatively recent custom can become treated as if it were age-old tradition passed down for generations. One thinks of a lot of wedding 'traditions', most of which have only popped up in the past 150 years and yet are often treated as if they were sacrosanct with all the benediction of antiquity.
Pope Francis recently made a change to the liturgical law of the Church. Under the current liturgical regime, it is an option to have a footwashing, the Mandatum, on Holy Thursday during Mass in order to represent Jesus's own footwashing of the twelve apostles after the Last Supper. Previously the rubrics explicitly stated that this Maundy Thursday footwashing should be of men, viri selecti. (It's generally assumed that twelve have to be chosen, but unless I am just missing it, the current Roman Missal does not require this.) In fact women have also been chosen for this option for years and years now, despite the fact that the statutory requirement was pretty clearly males -- viri selecti was officially interpreted by most bishops as not excluding women. Francis changed the literal requirement to allow anyone to be chosen from the People of God, Qui selecti sunt ex populo Dei. It's worth noting that choosing any women (or any men, for that matter) is an option, not a requirement, just as having the Mandatum rite at all is an option, not a requirement; and it appears only to apply to the Ordinary Form, not the Extraordinary Form.
Of course, in these days of endless liturgy wars, one gets the standard kefuffle. The worry that's most worth taking seriously is one that goes like this. The footwashing symbolizes ordination to the priesthood; Jesus doesn't wash the feet of just anyone, but of the twelve apostles, on a night in which they are initiated into an extraordinarily new way of doing things. Holy orders cannot be imposed upon women under any circumstances, so it makes no sense whatsoever for priests to wash the feet of women in the Holy Thursday footwashing. It destroys the traditional symbolism.
Now, it's important to grasp that the idea that this particular footwashing (there are other kinds not in view here) is most appropriately treated as a symbol of ordination is not a bad, not a foolish, not an unreasonable interpretation at all. (This is a fairly nice presentation of it.) A great deal of what goes on Maundy Thursday is clearly bound up in the nature of holy orders; a great deal of this part of the Passion narrative is quite clearly concerned with matters that teach us about holy orders; the use of the footwashing in this particular Mass quite reasonably suggests matters concerned with the vocation of holy orders; and it actually makes a fairly good symbol of certain aspects of holy orders, which in a sense is the sacrament of the humility of Christ. You can perfectly reasonably suggest that in the context of this Mass it would be better to treat it as a symbol of holy orders, which it could suggest and has increasingly been taken as signifying, and that it would have been better to teach this particular symbolism and enforce the prior law, than to change the law to fit the common custom.
But the interpretation is not traditional. It has grown up within certain groups within living memory. If you look at Augustine, Chrysostom, Aquinas, Bonaventure, it's difficult to find anything that even remotely suggests it. The consistent interpretation of the Church Fathers of the Holy Thursday washing of feet is Christological: it represents the humility of the Incarnation and provides a moral example to all Christians.
And the rite's place in the Mass is quite recent. There was a separate rite of footwashing in the Tridentine liturgy but it was of restricted application and occurred outside the Mass. Prior to this there seem to have been some cases of its actually being incorporated into the Mass, particularly among Benedictines; but for such cases there is nothing I know of to indicate any association at all with holy orders, which would have been rather odd in that context, in any case. The placement of the washing in the Mass itself only came about in 1955, when Pius XII put it after the homily. If done outside of the Mass, however, there is very little to suggest any symbolism of holy orders; it just becomes like all other footwashings, although one that happens to be especially appropriate for the day. And those washings are concerned specifically with reminding people of Christ's humility and their responsibility to take His example to heart; there's a reason why it was generally expected in some parts of the world that kings and queens would wash the feet of their subjects, and bishops of their priests or of the poor, on Maundy Thursday. The fact of the matter is that rites and ceremonies of footwashing, even on Maundy Thursday, have rarely been important enough to bear much more symbolic weight than that of the importance of humility. You can find cases where it could possibly bear such meaning; but its status and practice has never been stable enough for this to be a consistent implication.
What's more, there seems to be no sign that Pius XII in his introducing it into the Mass, saw it as any kind of symbolic sign of orders; it's described as providing a reminder to all Christian faithful that they should abound in charity.
None of this changes the argument for the priesthood interpretation, which has to be considered on its own merits. It's not the case, though, that it is any kind of traditional interpretation. It's a relatively new one, less than a century old, that arose out of twentieth century liturgical reforms. To claim that it has traditional roots we have to say that it is restoring a symbolism that fell out of sight and of which there appears to be no direct trace.