But, there are two reasons that Bush's military record are at issue. The first is fairness - Bill Clinton was called a "draft dodger" throughout his entire presidency. That charge, which I don't think Peter Jennings ever called "reckless," is untrue if we're keeping with the legal definition. And, if we're referring to the general idea that "Clinton tried to avoid going to Vietnam," then almost every Republican in congress (and plenty of Democrats) is a "draft dodger."
But, that's a secondary reason. The primary reason is that Bush has made his military service an issue. If in 1999 Bush had gotten up and said "You know what? I was grounded because I refused to take a required physical. Then, I transferred to Alabama and didn't show up much. I'm not proud of it, and eventually I managed to get an honorable discharge, but it wasn't a shining moment in my life," then I'd be fine with the whole thing. I can't speak for other people, but that's my take.
But, he didn't. He claimed to have flown for several years in Texas after his training. A lie. He used his Guard service to claim he learned important life lessons - from his autobiography (thanks to Flitcraft).
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I can remember walking up to my F-102 fighter and seeing the mechanics there. I was on the same team as them, and I relied on them to make sure that I wasn't jumping out of an airplane. There was a sense of shared responsibility in that case. The responsibility to get the airplane down. The responsibility to show up and do your job.
He then used his military service to justify the whole Flightsuit Boy Goes to the Aircraft Carrier Day, as his administration did their best to imply that he not only flew the plane but personally landed it (no, they never said so, but they were coy enough to encourage speculation and confusion). So, he made an issue of it - and, the issue is honesty. Simple.