High court strikes down key parts of Arizona immigration law

http://nbcpolitics.msnbc.msn.com/_n...own-key-parts-of-arizona-immigration-law?lite

The part of the law the justices upheld requires police officers stopping someone to make efforts to verify the person’s immigration status with the federal government.

The justices struck down three other parts of the law:
One making it a crime for an illegal immigrant to work or to seek work in Arizona;
One which authorized state and local officers to arrest people without a warrant if the officers have probable cause to believe a person is an illegal immigrant;
And one that made it a state requirement for immigrants to register with the federal government.

In what world, and for what reasoning, would the justices strike down the part about the law that makes it a crime for an ILLEGAL immigrant to seek work.

Isnt the point of being illegal, that you shouldnt be here to begin with?