I am also unsure as to whether this is a good decision, but not because of a perceived mismatch between training and mission. While they haven't given a lot of specifics about the units deploying, there is no large body of personnel organized and trained for this other than certain units of the military. The CDC (which has been on the ground from the beginning) doesn't have anywhere near the resources and something like the Peace Corps is far, far from prepared for somethring like this.
Bear in mind that, at the top of the list of our national security concerns is biowarfare, and Ebola is one of the most feared agents in a potential enemy's arsenal. For that reason, the military has been training special units to cope with biowarfare attacks. Since a biowarfare attack is identical in any practical sense to a natural outbreak, those units are really the only such bodies of men and women available who have the training and resources to handle something like this! No other country except maybe Russia or China have invested as much as we have for this kind of scenario. These troops may well prove to be the best possible first responders on earth to this kind of situation.
Plus, this will undoubtedly prove to be an unprecedented opportunity to test out responses and develop better protocols. It may well turn out that someday we face a bio attack in the U.S. and find that countless lives have been saved due to the lessons learned in the real-world deployment/test bed that was the Ebola outbreak of 2014. I don't see this as in anyway an example of s being the worlds policeman - this isn't a conventional war and the enemy isn't even from our own species. Stopping outbreaks like this are a direct national security issue, as we are as threatened by disease outbreaks just like everyone else -- disease threatens us all equally, and it is especially important to contain epidemics of diseases like Ebola because every day the virus spreads is another few billion opportunities for it to pick up new characteristics and mutate. If that stuff goes "airborne" (as the media describes aerosolization) then Ebola could become a "slate wiper in humans," to borrow a quote from one of the first scientist to devote his career to studying this strain of hemorrhagic fever.
I agree there are some political elements to this that make me uncomfortable, but for the reasons I just outlined I am not sure that I oppose it either.