From Oxford Languages:

Profession (noun)
1. A paid occupation, especially one that invilves prolinged training and a formal qualification. "his chosen profession of teaching"
2. An act of declarint that one has a particular feelint or quality, especially when this is other case. "his profession of delight rang hollow".

You don't need a certificate to be a wet nurse or any training, certainly not prolonged. Women who were wet nurses received some compendation, but being a wet nurse was not their sole occupation. At absolute best, it can be considered gig work in modern terms because it's also not something you can continue doing. You can only do it while you're producing milk. That's not something that happens consistently or that you have much control over.

So. Wet nurse was never a profession like medical nursing is, where you have training, go through a qualification process, and receive compensation for.

Again, the author never said that there weren't female nurses prior to Florence Nightingale. She said that once nursing became a profession, it was predominantly a male profession until Nightingale's work opened it up to women.

I'll point out that being a woman or group of women who establish a hospital does not automatically equate to staffing open nursing positions with women. Not in Rome, not in the Catholic church, or anywhere else. What matters is who the nurses in those places were and if they were acting in a professional capacity or not, including receiving compensation.

Sorry dude. Words mean what they mean. You don't get to rewrite the dictionary just to be anti-feminist.