Too bad it's a bunch of bullshit. The REAL reason is because we had a bunch of freed slaves with no country, a bunch of Native Americans with no country, and the natural born citizenship question needed to be answered. Notice Senator Howard (author of Amendment) doesn't state that its legislative intent is the blanket granting of citizenship to anyone who pops outta their mama on US soil.
"Every person born within the limits of the United States, and subject to their jurisdiction, is by virtue of natural law and national law a citizen of the United States. This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons. It settles the great question of citizenship and removes all doubt as to what persons are or are not citizens of the United States. This has long been a great desideratum in the jurisprudence and legislation of this country."