Why the overall disapproval?
Im afraid I have only a silly and somewhat crass answer... it verbalizes my opinion.

Why? Because even if you put a cherry in the middle of a shit sandwich, its' still a shit sandwich.

Many a horrible leader have done something worthwhile..... however a single something, that cherry as it were, does not make up for the overall actions (or lack of actions ) for said leader. And I use the word "leader" as only a general commonly understood term, not in any way as an accurate description of our current president.

I've read the article a couple of times now, as well as similar articles on The Daily Beast, and in The Atlantic, and Stars and Stripes, and I've noticed something.

There are three words in the English language that reporters, along with many other people, seem to confuse for synonyms: "compliance," "acceptance," and "tolerance." They don't mean the same thing. "Tolerance" is what people should do out of basic human decency and common courtesy for one another. "Acceptance" is a matter of individual conscience - there's no way any of us can really peer into each other's hearts and mind to tell just what some one believes with 100% certainty.

"Compliance" is what the military can dictate to its personnel, and the truth is, that's _ALL_ it can realistically dictate with any certainty - there isn't a policy or regulation in the world, no any amount of fiat by any commander that can successfully mandate "acceptance."

You can demand compliance with policies that support tolerance, and that encourage acceptance (at least enough to allow people to work with people they might not socialize with otherwise), but you can't actually dictate the terms of anyone's conscience. I think the problem is we assume people are much more blank slates than they really are.

I find it interesting that some of the reasons cited for "dissatisfaction" include acceptance of homosexuality in the ranks and aggressive pursuit of sexual harassment and its reduction in the forces.
Seriously, if you are unhappy because the guy next to is gay or you can't rape the service member of choice, you probably shouldn't be in the service, in which case, I really don't give a damn about your opinion of the President.
Next, the implication that the dissatisfaction is a result of Service Members over all ignorance of the American political process and who is truly responsible for the changes in Service Members fortunes over the last 6 years. Veteran Care has been stonewalled by Congress. Closure of GTMO has been stonewalled by Congress. Downsizing was demanded by Congress by not continuing the expansion on the services granted in 2003. Many of these changes in fortune were the result of a Republican House rather than the will of the President.
Morale is also deteriorating because of a perception of inequality among the ranks. High profile cases continue to be tried in the court of popular opinion absent of significant facts. GEN Petraeus, SGT Bergdahl, GEN Sinclair, and LT Clint Lorance as well as anecdotal comparisons of what happened to one friend or another. Summary court martials and discharges are increasing as part of an effort to reduce numbers. Many officers generally respected by enlisted because they took the mission of troop welfare seriously, are not making the post drawdown cuts because they weren't as "effective" at getting things done are another consideration.
As much as we may want to blame the CinC for the current woes of the services, there is no shortage of blame to go around, and the services themselves are as much to blame for the current situation as anything else.