As an aside, I can kinda understand vegetarians eating eggs because chickens will just lay them and you either eat them or they rot, but vegetarians who eat milk have no moral ground to stand on.
She eats plenty of dairy, as nothing died, and considers herself vegetarian. She has in fact never eaten meat once in her life yet you have entirely discounted her moral standing.
Your argument sounds a lot like No True Scotsman.
Speaking as a vegetarian myself.
For example, I often imagine what our carbon budget (and theoretical karma budget) would look like if we could get more people who are pro-animal welfare (and people who are concerned with climate change,) to accept the idea that getting a few billion people to eat less beef might be more beneficial than getting a few million to eat no beef.
There is a really interesting paper on this topic which often comes to mind titled "The seductions of clarity." [0]
There is also an interview by Sean Carrol with the author of that paper titled "C. Thi Nguyen on Games, Art, Values, and Agency" [1]
[0] https://philarchive.org/rec/NGUTSO-2
[1] https://www.preposterousuniverse.com/podcast/2021/10/18/169-...
A cow must get pregnant to begin producing milk, but because we breed dairy cows for milk they produce much more than the calf needs anyway. Male calves are doomed either way to be slaughtered by the realities of how the industry works, but there is no requirement that things be this way.
Eggs are similar in that they don't technically require any particular cruelty, but the realities of how the industry functions means that male chicks are killed shortly after birth. Again, it need not be this way.
One view of how this informs our diet is that eating eggs and dairy are not necessarily cruel, they are just cruel in practice. Whereas meat consumption necessitates the killing of animals.
Loads of calves die to supply milk, and cows are kept in a near permanent state of either being in milk (and missing their calves) or pregnant.
I really don't mind what anyone eats or drinks - but anyone who claims to be vegetarian 'because of the animals' - but then consumes dairy, is on pretty weak ground.