College administrators suspended lee loughner after they became concerned about loughner's potential to commit dangerous behaviors. why didn't authorities arrest him?

The correct answer is:

Loughner did not make any overt threats against anyone.

Jared Lee Loughner is an American mass murderer who shot and critically wounded his primary target, U. S. Representative Gabrielle Giffords and killed other six people in the Tucson shooting (January 8, 2011). He later pled guilty to 19 charges of murder and attempted murder.

Despite having shown previous disruptive behavior he wasn't arrested until after the shooting because no open threats were made.