President Trump wants to end birthright citizenship, i.e. the idea that one who is born on American soil is automatically an American citizen.
Regardless of the merits of birthright citizen, no President can or should have the power to alter long held constitutional meaning. The 14th Amendment has long been interpreted to mean someone born in the United States, excepting those formally representing foreign governments, automatically become citizens by virtue of birth in this country.
You can feel free to claim the interpretation is wrong, but that is how it has long been done and Congress, which has the power over immigration, has never changed it.
Allowing any President to change any long held interpretation of the Constitution is a dangerous game that no Republican should want any President to have. This President and his party will not control the White House forever. Imagine letting Barack Obama interpret the "free exercise of religion" clause to declare, as he tried before the Supreme Court, it only means worship.
Article 1 of the Constitution allows Congress to set immigration laws. Congress has declared that all people born in the United States and subject to its jurisdiction are citizens. If you argue illegal aliens are not subject to the jurisdiction of the United States, then you need to stop charging them with crimes under American law and remove them from the United States.
Likewise, if your argument is premised on "subject to the jurisdiction" language in the 14th amendment, the President does not have unilateral authority to change the meaning via an executive order. This is a dangerous, autocratic power that the Founders did not intend to give a President. What is so deeply hilarious is watching some segments of the right who've long thought Marbury v. Madison was a judicial overreach suddenly claiming the President can, by executive order, change long standing constitutional interpretations.