The Cuban adjustment Act (CAA) is a law that gives Cubans citizens, their spouses and children the possibility of getting a green card if they have been physically present in the US for at least one year and have been admitted or paroled (i.e.: entered with a visa or a parole document).
A law is an act of congress, not the president. The famous “Wet Foot; Dry Foot” phrase reflects not a law but a policy; a way to enforce a law by the president of the United States. In fact the words “Wet Foot; Dry Foot” are not written in any code or official document. It is a colloquial way to describe certain policy guidelines issued by the executive branch as to how to apply the CAA law.
Thus, when Obama cancels the Wet Foot; Dry Foot policy, he is not cancelling any law, and therefore he is not cancelling one word in the CAA.
What Obama did does not affect at all Cubans immigrating to the US with a visa or a parole document. It does affect those Cubans trying to enter the US illegally (through the US coast or through the borders).
Why did Obama do this? There appears to be three important reasons. First, end illegal Cuban immigration. Second, the change makes a disincentive for those involved in Cuban human trafficking and those immigrants who dare to take such a risk. And three, an agreement with the Cuban government (in an effort to normalize relationships with Cuba) for Cuba to take back Cuban criminal immigrants the US constantly removes and that Cuba refuses to take. Ending the Wet Foot; Dry Foot was apparently part of the deal.
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 There are also state laws that are made but state legislatures but since immigration law is federal law, immigration laws are only made by the US Congress.