Remember in middle school or high school, there was always that one kid that wanted to cheat off your test? He/she would never study, never put any effort in anything, yet felt entitled to pass everything? Well, I think that's how hardcores feel when they see casuals and gamers asking for an easy mode. They see laziness, and they learn to despise it.
Now of course games are just that, but you can't deny some people wanting to treat them as if they're something more important. There are hardcore gamers that enter competitive gaming and actually make money from it, so like it or not, gaming can never have a very serious competitive tone to it where it's not going to lower it's difficulty to allow more to enjoy.
Of course this is only with some games, a lot more out there can just be casual games, children's games, or not even really games at all... and more like interactive movies (Heavy Rain).
But some gamers treat games seriously, and want it to become something more serious whether who likes it or not. Not all gaming, but some of it. Pretty sure a lot of people that like Dark Souls.
When you start asking for an easy mode, they see someone that just wants to skip on by like that kid that wanted to cheat off your test in high school. And they hate them for it.