I remember back during the betas, I thought the personal story quests were too difficult. During launch, I can’t say the same except for two missions to date so far. For the record, I was playing an Elementalist as my first character, no, my armor was not up to date all the time, and I was usually kitted in blues, with a couple of greens, as I wasn’t willing to spend the extra money on a green over a blue when it would just get replaced in a few levels.
The two missions is the Skritt one where I had to fight off the destroyers, since my build at the time was rather focused on Burn damage, and I had not gotten into the habit of carrying other weapons (was using a Staff at the time), I got my butt handed to me. Multiple times.
The other is the Battle of Claw Island. But, this is more a psychological issue than an issue with “not designed for non-tanking classes”. When I run into enemies that are worth zero exp, and zero loot, I tend to want to ignore them, and rush past them. Which is a bad idea on this map, but they continually spawn and I just want it over with since the risk/reward ratio is not in line. I get that all of the enemies need to be there to make the battle epic, but having the enemies do full damage and provide no reward is just wrong. I actually found this particular story mission difficult with a Warrior kitted in Exotics, but, again, psychological factor of me wanting to rush and yes, that means run past enemies ignoring them and having a large group trying to assault me instead of taking my time and killing a path.
All the other story missions that I have done, which includes the racial story lines for Human, Norn, and Sylvari, and all three Orders, were far from being “too difficult”. While I feel the suggestion of googling is a good idea, I never had to because I would always look into breaking down the combat, and answering that question of “What am I doing wrong?”. One should not expect to have a static build of two specific weapon sets, a single heal, three utility and an elite to be able to complete all content in this game. Guild Wars 2, just like it’s predecessor, is built upon “Counters”. Everything has a counter. And when your “static” build runs into it’s “counter”, you’re in for a world of hurt if you haven’t learned how to adapt.
I also want to applaud Jeffrey for coming in here to comment about what he uses to playtest with, and that he doesn’t use a downscaled 80. 
I’m sure there will be some who won’t believe him or feel that the content is geared around thieves now, but really, the story stuff can be done by any class. Just bring what can counter the enemies you’re fighting. Figure out how the enemies are doing damage, and learn how to mitigate it best for your class.