Having already served during time of war, I'm actually exempt from it either way. But you have a fundamental flaw (more than one actually) in your statement that requires addressing.
First of all there needs to be options of civil service instead of military, since there are some true pacifists out there who would be happy to serve their country, but not harm others in the process. Second, cowardice probably plays a role in some, but not in as many as you'd think. More likely they are taking the considered (and correct) stand that while a defensive draft or mandatory civil service might be acceptable, an offensive draft (especially while a dictatorial empiracal regime holds control of the country) is something to be avoided. Lastly, the government doesn't make decisions for the people of this country, however much everyone would like to think they do. They control only their own lives and make their own decisions...it's up to us, as individual citizens, to make our own decisions about their decisions. The decision to serve, or not to serve, is one we each have a right and responsibility to make after careful consideration of all facts and possibilities and no force on earth can ever take that from us (though we can offer it up without resistance if we so choose). Upon joining the military, if that was your choice, you would be required to take an oath to protect NOT the government or it's employees, but the constitution and ideals of this great nation. Once you take that oath you'd be hard pressed to uphold it while under the command of the current administration (just my opinion, yours can vary).