EDIT: Why the downvotes? I'm asking a genuine question. How did I manage to offend?
People also want temporary residence to be given to asylum seekers, as specified in the UN Convention on Refugees. Allowing someone to remain in the country is not the same as granting them citizenship. It is also not the same as entitlement to benefits, entitlement to vote, etc.
To be fair here, those who support the detention regime are also generally in favour of deportation. However, current US laws require amounts of due process (to evaluate the claim on its merits) that -- combined with current administrative resources -- result in a slow timeline for hearings and deportation.
Therefore, immigration advocates argue for continuing the past practice of release on bail-like conditions, whereas restrictionists argue that such release is itself a threat (e.g., claimants can 'disappear' as illegal immigrants) and detention is necessary notwithstanding the human cost.
In the meantime, there is also evidently an informal argument that detention itself should act as a deterrent, as weaponized cruelty. This argument is legally and morally reprehensible, but as far as I know policymakers have not officially made it.
Literally none of those are "giving citizenship to everyone who wants it". To take your eventually example to the next step, if their children's children have kids on US soil, they will automatically be US citizens. By your logic, the existing US Constitution is "little different" from the same policy.
8 U.S. Code § 1158. Asylum Any alien who is physically present in the United States or who arrives in the United States (whether or not at a designated port of arrival and including an alien who is brought to the United States after having been interdicted in international or United States waters), irrespective of such alien’s status, may apply for asylum in accordance with this section or, where applicable, section 1225(b) of this title.
False dichotomy.
"A situation in which two alternative points of view are presented as the only options, when others are available."
There was never really a crisis until we created one.
Recently, Trump's DOJ reverted policy back to the way had been for decades. This has reduced the incentive to send women and children first because domestic violence/crime are no longer grounds for asylum claims.