It appears that a lot of Allied commanders such as Bradley had personal issues with Patton as a General. Why did he earn this reputation?
I think you have to remember that Patton, for all his considerable skill, could be a thoroughly infuriating figure. Arrogant, rash, abrasive, impatient, and often intolerant of anything less than an almost reckless abandon for action the best that can be said about him is that he won, and that's probably all he or Eisenhower cared about. And, while it's true many American and British generals disliked him personally, most of even his staunchest adversaries admired his skill and ability. His reputation amongst the Axis forces was because, in many ways, he was the most successful emulation of their type of armored campaign. His ability to conduct brash and often reckless maneuver with great success at the expense of multiple German commanders earned him a thorough and almost universal admiration and respect as the best the Americans had to offer. All in all it was mostly his personal baggage that earned him a foul and sometimes unfair reputation and led many to downplay his professional successes due to personal grievances.
Mostly because the German high command only got to see a man with many victories under his belt while the US generals had to deal with his actual personality. He was someone who could be easily disliked. especially by his own soldiers and anyone who told him that his strategy wouldn't work. He knew he was good and assumed everyone else was wrong. So it gave him a bad reputation with his fellow generals when he looked down on them and their ideas for strategy on the western front.