By making the distinction of immigrants as being legal or illegal you get toi bypass the fundamental question. Why should these people not be permitted to enter the country legally? If we allow them to immigrate legally then you no longer get to fall back on their being illegal immjigrants as the reason why they shouldn't stay.

see the arguemnt is circular.

Q) Why shouldn't these people be allowed to live here?

A) Because they are criminals.

Q) What crime are they committing?

A) Being here illegally.

When you open immigration to all people (excepting specified people with criminal or terrorist backgrounds) then the distinction between legal and illegal immigrants mean something, since the only people who would have to immigrate illegally would be criminals (people who have committed serious crimes) and terrorists. Protecting the morders will be easier because when someone is sneaking across the border you know they are a criminal or a terrorist, not just a migrant fruit picker looking for work.