The 14th Amendment contains the words “subject to the jurisdiction therein” specifically to exclude those who not subject to US laws, i.e., illegal aliens. If you are an illegal alien or a diplomat, you are not subject to the rights bestowed citizens under the Constitution. There is nothing confusing about it.
If the founders meant that everyone born in the US is automatically a citizen, they would not have added those very specific words to the amendment.
Imagine the case in the future of: "...your parents were radical, anti government activists in a tea-party movement, this is sedition, therefore they gave up their citizenship and we have decided your parents, when you were born, weren't 'subject to the jurisdiction thereof' so we strip you of your citizenship...