Reason 1. Christianity and religion in general is cheapened when it feels that it needs governmental endorsement. If a Christianity isn't strong enough to stand on its own two feet without the United States government holding its hand, then it's apparently not a very convincing religion. This, however, is not the case. Much of the appeal of early Christianity was that it was a counter-cultural movement. This same appeal may be much of the draw of minority religions which many Christians fell they are in competition with. Quite simply, it might help Christianity if the government was indifferent to it. Much of early church history is the story of persecution by government authorities.
Reason 2. Jesus Christ said that his kingdom was not of this world. (John 18:36) There are numerous verses in the New Testament that state Christianity is not a part of this present world. Why should Christians worry about having a kingdom in this world when Jesus Christ himself did not want a kingdom in this world?
Reason 3. Religion and government both tend to corrupt themselves when they ally with each other. The government will use religion mercilessly to gain political support. This has been seen numerous times in history. The Crusades of the Middle Ages raised the Cross as a banner, and more recently the United States was fighting the 'godless' communists during the cold war. Presently, I see some government officials using language that borders dangerously on turning the war with Iraq into a Holy War. It isn't wise for religion to willingly put them into a position to be used by the government.
Religion can also corrupt the government. Rulers who have somehow gotten into their minds that they have a divine right to rule tend to be some of the worst tyrants. Take the case of Nicholas II of Russia. If he had been willing to step down in 1905, or even to allow the Duma to actually do something, history might have taken an entirely different course. Nicky had this idea in his head, however, that God wanted him to be in charge of Russia, and he wasn't about to step down as Tsar or give up any of his absolute power. The rest is rather violent history.
Reason 4. Which form of Christianity would the Government ally itself with? If it chooses to join forces with strict fundamentalist Christianity, women can kiss their jobs and blue jeans goodbye, and I am not making up. While this may be an improbable scenario, it's not an impossible one. The world has seen what can happen with theocracy.
Reason 5. If Christians wish to follow the golden rule, then others should be granted the right they claim for themselves. For instance, most Christians I know who want "Under God" in the pledge would object strongly to the government endorsing atheism. If we want the right to believe; we have to allow people the right to disbelieve. This is legally and Biblically right as I see it.