This is actually part two of a short series. Here's part one. The first video focuses on the reaction to the work of feminist Anita Sarkeesian, but this video makes some more general, interesting points about why simple remarks like "I'm an atheist" or "I don't drink" can sometimes offend people.
I think this analysis is very helpful for personal introspection re-evaluation of one's opinions, and also for understanding the reactions that you will often get for discussing particular kinds of issues both online and offline.
there's this thing called transactional analysis. It was bigger in the 70's but fell out of style, but some of the core concepts are neat.
It breaks us into three ego states - the parent, the child and the adult. When we interact with other people, we each take on one of these ego states. In rational conversation we might both take on adult, in play we might both take on child, in learning one person might take on child while another takes on parent. These are learned states that help us quickly determine the power structure of an interaction.
I think that when people are in these situations where someone say no, they don't do that thing, it subtly changes the dynamic of the conversation. The first person, the one who offered the thing, sees the transaction as adult to adult. Once the other person says no from a moral standpoint, they are seen as taking a parent role. Now we're in what's called a cross transaction, where one party was expecting a certain ego state but got another.
There are really only two reactions to this crossed transaction. The first party could hold fast in their adult ego state and say, "cool", drop the perceived slight and move on. The other option, the option chosen by the loudest of the internet, is to make the transaction even again. They respond to the parent ego state by taking on a child ego state and by throwing a digital temper tantrum. They see the morality of the other person as a characteristic of an adult state and finish the game by taking on a child state.
The theory is that this is a remnant of childhood learning. The folks who lash out were, as children, subjugated to moral authority from the parents in their lives (maybe not literal parents, but people who played the role). Once that stance is taken again in their adult lives, they slide from their stance into a child state. I think this is even easier online because the people who yell and fuss use the internet as a playground for their child state, so the transition isn't a state change, but a change of mood for the state they are already in.