Friend, I see you have limited knowledge about international law so I'm going to leave it here. I am not a teacher so I won't explain it to you, I ain't got the time to anyway, but I suggest you do some research, get back to me then and we can discuss this if you like.
The U.S. is bound to accept asylum seekers in both international and federal law. The U.S. is definitely bound by international law, it has ratified these agreements, so it certainly is bound by them. I'd recommend reading this: https://ijrcenter.org/refugee-law/
EU-policy states that when an asylum seeker enters any country in the EU, that is the country they need to seek asylum in, they can't wander through the EU to a different EU country to seek asylum. If they do they are returned to the first EU-country they entered, seeing as getting residency in one EU country entitles you to freely move within the whole EU.
The the states of the U.S. are much more integrated than in the EU, thus this policy is not really useful there, but one could compare it to if you enter the U.S. through Texas you are not allowed to move to another state to seek asylum.
Anyhow have a good day Taleladar.