I am hugely pro-breastfeeding, and I get the goal of supporting/educating moms. I mean in the past, moms were discouraged from it. Many decades/maybe a century ago there was even a stigma attached to breastfeeding. In an ideal world everyone would do it and nobody would have difficulty.
Trouble is, we don't live in an ideal world.
I feel like the pendulum has swung too far. Shaming women and making them feel less of a mother does not help, especially in such an emotionally delicate time as the postpartum period.
Ideology aside, the baby needs to eat. Sure keep trying if you want to, but in the meantime you can't malnourish the baby on a principle.
And thanks to modern innovation, they are making formula more like breastmilk all the time.
I also think the it's-natural-therefore-it-should-be-easy idea is oversimplified. I have 5 kids and breastfed all of them. I read everything I could get my hands on during my first pregnancy. One thing that every book said was "if you do it properly, it should not hurt." Imagine my surprise when for the first two weeks it felt like this toothless person was chewing my nipples off!! It was like nursing a piranha. My midwife (also an IBCLC) checked her latch, assured me it was fine... I kept going because I am that stubborn and it got better. Not what your wife experienced, but it's a pet peeve, setting up unrealistic expectations...which creates feelings of failure when those expectations are not met.
Good for you for standing up for your wife. I'm sure this is difficult for her -- she's putting all this effort in (and pumping is a huge effort!) That LC added insult to injury with her, uh, "coaching" style. And again, putting an ideology ahead of the baby's immediate need for food. You seem like an amazing husband and I'm sure are a great dad too!