ImageShack removed images that became too popular, which created maximal outrage with the most people, just as content was going viral. Images hosted on ImageShack would randomly get corrupted, and it'd be difficult to reach support to fix this. ImageShack was annoying. You'd try to go directly to the .jpg URL and it'd load the HTML website with lots of ads. In order to upload to ImageShack, you'd have to register an account and potentially pay money.
Imgur was a breath of fresh air. They didn't do any of those things. It was just the simple reliable free image upload service people wanted. So it took over ImageShack's role almost overnight. Imgur eventually rolled in their own exploitation, but they did it a lot more moderately than ImageShack.