Julissa Arce, an undocumented immigrant and former Goldman Sachs executive, said the University of California was correct to allow illegal immigrants to receive preferential treatment versus out-of-state citizens.
The university system is capping the number of out-of-state students at 18 percent, while illegal immigrants living in California are not capped.
Arce said that the school's regents are supposed to help "California residents."
She accused Carlson of having a "lack of understanding" about the issue.
Carlson said it was Arce who wasn't understanding the idea that illegal immigrants now take precedence over American citizens.
"California is not a country, it's a state, it's one of 50 of those," he said.
Carlson said he realized Arce was using the term "residents" rather than "citizens."
"People that are illegal in one state are illegal in all states [they reside in]," Carlson said.
He asked Arce to name another country that would allow people from elsewhere to take precedence over citizens, no matter their native province.
Watch the fiery debate above.