Birthright citizenship does exist. Under the current Constitution and federal law, those born in the U.S. to U.S. citizen parents or aliens permanently domiciled in the U.S. have a claim to birthright citizenship though that does not necessarily make the latter natural born citizens for Constitutional purposes.
Similarly, one born abroad to U.S. citizen parents may be defined as natural born citizens by statute but that does not necessarily imply that they are natural born citizens for Constitutional purposes.
Quoting the U.S. Department of State:
"In any event, the fact that someone is a natural born citizen pursuant to a statute does not necessarily imply that he or she is such a citizen for Constitutional purposes."http://www.state.gov/documents/organization/86757.pdf
“Under the current Constitution and federal law, those born in the U.S. to U.S. citizen parents”
And where does the constitution specify this?
“Under the current Constitution and federal law, those born in the U.S. to U.S. citizen parents”
And where does the constitution specify this? The constitution doesn’t give this distinction. This is the problem. You are reading into it something that is not there.