Hagel has made a career of alienating what potential friends and allies he might have had. Through UNL, I've had the opportunity to try to get help from Hagel on various matters of what might be considered constituent service; things like interceding with the State Department to overcome obdurate bureaucratic obstacles on student visas, etc.. He consistently refused to help. UNL's administration ended up completely ignoring him when lobbying for earmark requests, because they knew he would do nothing. If all of this were out of principle, I'd admire it. But there is no evidence Hagel philosophically believes that it is wrong for the legislative branch to intervene with the executive branch to accelerate certain operations, or that earmarks are wrong. He's been happy to vote for all sorts of other federal pork. He just didn't seem to feel it was worth his while to help UNL.
It's not just his failure to positively help his actual or potential constituency. Hagel has gone out of is way to insult Republicans and particularly conservative Republicans; calling us 'disgusting' for trying to use the debt ceiling as leverage to force a reduction in government spending, a goal he theoretically believes in; endorsing Democrats for national and statewide office, etc.. He's alienated pro-Israel Americans by a long series of votes and actions on Iran and Israel. He could have voted against Hormel without opening his big mouth and calling him 'openly, aggressively gay'.
I may not have accumulated all the wisdom I could have in my nearly 55 years (there's an understatement), but I have learned (though perhaps not sufficiently internalized) that you make too many enemies and lose too many friends simply doing the things you have to do, particularly if your politics departs from the bland middle. Going out of your way to make more enemies and (in Hagel's case) lose a whole lot of friends is simply stupid.
And honestly, after thinking about this for a couple of weeks, I think Hagel's besetting vice is stupidity. He voted for the Iraq war, and then turned against it as soon as it started going bad. He supported pulling out as soon as the insurgency developed, with no consideration that America -- in part through his own vote -- had made a commitment, and we would break our word and irrevocably damage our national prestige by doing what he advocated. He opposed the surge, and even now refuses to admit it was the decisive factor in the defeat of the insurgency and in gaining some semblance of a positive result. Refusing to admit you're wrong is in my experience one of the true markers of stupidity.
And getting beyond all the antipathy created by Hagel's own actions, that is what I think disqualifies Hagel: he's just not smart enough for the job. Sometime, a penchant for opening your mouth and disputing the conventional wisdom in crude language isn't a sign of forthrightness and out-of-the-box thinking; it's a sign you think dumb things and you are too obtuse to realize it is better to remain silent and be though a fool, rather than speak and remove all doubt.