I've read that the passenger was travelling with a child and a baby, as well as the dog. Her journey would have been pretty stressful under the best of conditions. Deplaning would not have been an attractive prospect, especially as she could expect to be asked to put the dog in the locker in any alternative flight with the same airline.
I think she was not well-placed to sustain an argument with the FA. Anyone who's flown with a small child and a baby will know how stressful and preoccupying it is.
However, I'm also curious to know how airlines deal with dogs being allowed to travel on flights with allergic humans? I'm extremely allergic to dogs, not quite epipen level, but enough to swell up and alarm people. I've been on flights where snacks were withheld because there was a passenger with nut allergy on board. What about a passenger with dog allergy?