A better question would probably have been--"Why don't ALL Americans DISLIKE Bobby Fischer?"--since I don't think you really believe that all Americans like him.
Personally, he's never given me a reason to dislike him. He didn't do anything any more outrageous than other famous figures. In fact, voicing unpopular opinions and having an exaggerated sense of one's own importance is practically a prerequesite of becoming a cultural icon. We EXPECT our heroes to be either crackpots or a-holes (Fischer, apparently, was both).
But hey, if we can overlook Charlie Sheen's flaws why shouldn't we overlook Bobby's?
Fischer sent Lombardy, his second, to draw lots with Spassky. That had to have been a planned slight to Spassky; Fischer's excuse for not going was he was sleeping.
No. Not "a planned slight to Spassky"; it's well documented Bobby Fischer stayed up 'til the wee hours of the morning and therefore regularly was a late riser. He often missed morning appointments.