Can I be terminated because of one incident in my 38 months with employer?

On 9/30/11, I had a meeting with the Director of an agency and the client working in their facility. The Director wanted to end the program with the client because he failed to perform his duties to the acceptance of the facility. The Director and I asked questions of this person many times and he sat there not responding and finally, in anger, stated some things that were not true. I called the client a "big liar" and went on to correct him about his statements and inform him that I had just complimented him two days earlier. The exchange was "heated" at times, but I DID NOT abuse him verbally during the meeting. On 10/3/11, I mentioned in a Group Supervision meeting that the client acted like a "tar baby" because he sat there in silence, I DID NOT cal him this term, but stated in the meeting that he acted in that manner. On 10/10/11, I met with the Executive Director and my supervisor and was told that I was being terminated because of the "verbal abuse" and term "tar baby" used toward the client (the client is white) & it violated the code of conduct. I worked for the agency for 38 months and had NO disciplinary action in all that time and there were no complaints from the 112 other clients I had worked with over the years. I was not given the opportunity to present my case, the only witness did not state there was "verbal abuse" going on in the meeting and the client DID NOT file a grievance against me, in fact, they did not know of the details of the meeting until I brought it up in the meeting on 10/3/11. I have applied for unemployment & been denied, we are now scheduling for a hearing because I refuted the statements of the employer. Statements from the witness at the meeting NEVER said I verbally abused the client & she did not make a statement until 30 days after the incident & the client did not file a complaint until the Director asked him to & also asking for "complaint" statements by those in attendance @ the meeting & only 2 out of 18 made any statement with one saying that I did state the client "stared at me like a "tar baby"", not that I called him one.