The 14th Amendment states that, "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside..."
What was meant as a protection to children born to former slaves has in the past several decades been used as a means to circumvent the our country's immigration laws. A child born to illegal immigrants is instantly afforded health care, an education, and if needed welfare assistance. This type of illegal immigration is by far the worse because it uses children as a pawn for bypassing the immigration process and puts an unfair strain on our social systems.
Adding the caveat that at least one parent must be a U.S. citizen puts the burden of social care back on the country of origin.