They Are Illegal... and They Are Aliens 

Georgia Latinos Object to 'Illegal Aliens' Label

"We do find that term very offensive and liken it to the 'n' word as well," GALEO Executive Director Kerry Gonzalez said, referring to the derogatory term used to describe black people.

Gonzalez is urging Georgia lawmakers to use the term "undocumented workers" when referring to foreigners who enter the United States.

Illegal at Dictionary.com (emphasis added):

il·le·gal
adj.
Prohibited by law.
Prohibited by official rules: an illegal pass in football.
Unacceptable to or not performable by a computer: an illegal operation.

n.
An illegal immigrant.

Immigrant at Dictionary.com

im·mi·grant
n.
A person who leaves one country to settle permanently in another.
A plant or animal that establishes itself in an area where it previously did not exist.

adj.
Of or relating to immigrants or the act of immigrating.

Now... put the two together and an illegal immigrant is a person who leaves one country to settle permanently in another and in doing so breaks the law. Now what exactly is offensive about that? Maybe the fact that its incredibly accurate is what offends them. That must be it.