I worked for a company in Illinois and I was hired through a Job agency, I started May 1 and was fired on May 9, due to the fact they said I was sarcastic to the HR Girls when I was filling out my paperwork, I was disruptive during training, and I made a

I worked for a company in Illinois and I was hired through a Job agency, I started May 1 and was fired on May 9, due to the fact they said I was sarcastic to the HR Girls when I was filling out my paperwork, I was disruptive during training, and I made a rude comment, to a co worker and hurt their feelings. I was pulled into the HR office on May 9th and was told they were letting me go. My boss was no where around when any of this happened. I did not get a chance to defend myself. Know they are denying unemployment, I was there for 6 days. Can they do this?