When twitter goes down, the site is filled with the image of small blue birds carrying a whale. The second twitter goes down the internet blows up with articles about twitters outage. This is no different then other mega services like gmail or facebook. The difference is how users react to it. No other service has this relationships with its customers. Twitter failing has become "cute" because of the fail whale.
The reason people can interpret this as cute, is because twitter is not a necessary service. It is a leisure service. Even though companies can indirectly use it to gain customers or advertise, it is still primarily recreation. This becomes apparent when, by contrast, a service like gmail goes down. Personally, when gmail goes down by work stops. I don't even receive that many emails per day (probably only a few per hour) but when gmail goes down I get up from the computer, because it has become synonymous with work. I don't think twitter will ever have this relationship with its customers.
What do you think? Do you get angry when you see the fail whale, or is something you can shrug off until the service comes back up?