Well, I oppose it because I like freedom, liberty, individualism, and peace.
Empires, Colonial Powers, conglomerates, commonwealths, and federations have all proven not to work. You cannot force hugely differing peoples together...and this is only done under a military-style dictatorship or an extremely strong econom. In the past and through today, tens of millions have died under these tenets...the Roman Empire, the Byzantine Empire, South Africa, the British Empire, the Spanish Empire, French colonialism and expansionism, the old USSR, Muslims in Europe, Abu Sayef in the Philippines, Iraq, Afghanistan, the old Yugoslavia, the Balkans, Chavez's rise to power in Venezuela and subsequent national socialism, Morales and Bolivia, the slums of Sao Paulo, Mexican immigration into the US, etc.....and on and on and on.
So, yes, I oppose global government on the basis that it forces masses of differing people to live together.....violently. However, I do support true multiculturalism and diversity in that sovereign nation's borders are truly respected and the people's cultures, religions, and ethnicity remain intact within those borders.