No it isn't, that's not what appeal to authority means. An appeal to authority is using someone's perceived authority to support an argument, i.e. "Actually you're wrong, because Elon Musk says" or "Um, no, do you have a PhD in this, like I do?" or some other attempt to override argument with the trappings of success rather than actual merit. I know this because I have a Masters Degree.
Mothers can be horrible monsters, like everyone else. It's not really your call wether this was "needlessly" hostile or simply an outburst against feeling addressed by a simplification that can be very hurtful when you're on the wrong end of it.
Someone said above they like when HN gets emotional; well no, when only positive emotions are allowed that's just being soppy.
So here's to people with a splinter in their paw, may you find peace.
edit: I don't have narcissistic parents, I don't think, I was drawn to this sub because of other people in my life; but it's a very supportive place, one of the parts of reddit that are purely awesome: http://www.reddit.com/r/raisedbynarcissists/ (notice how Mother's Day is quite the issue for a lot of people)