Based on the scant facts you provided, it is impossible to predict the outcome. Your chances will be better if your supervisor will attend the hearing as a witness on your behalf (telephonic appearances are often possible), though given that the supervisor still works there, it will take a strong person to testify against a superior at work.
The administrative law judge (ALJ) who hears your case will be more impressed by facts and evidence, as opposed to opinion.
To gain a better understanding of the relevant definition of "misconduct," you should read the precedent decisions on the Employment Development Department (EDD) website. The website is http://www.edd.ca.gov and you can find the precedent decisions at http://www.edd.ca.gov/UIBDG/. Obviously, look at the category for "misconduct."
*** All legal actions have time limits, called statutes of limitation. If you miss the deadline for filing your claim, you will lose the opportunity to pursue your case. Please consult with an experienced employment attorney as soon as possible to better preserve your rights. *** Marilynn Mika Spencer provides information on Avvo as a service to the public, primarily when general information may be of assistance. Avvo is not an appropriate forum for an in-depth response or a detailed analysis. These comments are for information only and should not be considered legal advice. Legal advice must pertain to specific, detailed facts. No attorney-client relationship is created based on this information exchange. *** Marilynn Mika Spencer is licensed to practice law before all state and federal courts in California, and can appear before administrative agencies throughout the country. She is eligible to represent clients in other states on a pro hac vice basis. ***
Under Unemployment Insurance Code section 1256, "[a]n individual is disqualified for unemployment compensation benefits if the director finds that he or she left his or her most recent work voluntarily without good cause or that he or she has been discharged for misconduct connected with his or her most recent work."
Relevant precedent defines "misconduct" as:
(1) A material duty owed by the claimant to the employer under the contract of employment;
(2) A substantial breach of that duty;
(3) A breach which is a wilful or wanton disregard of that duty; and
(4) Evinces a 'disregard of the employer's interests,' i.e., tends to injure the employer.
It is the employer's burden to prove misconduct.
Additionally, the Administrative Law Judge may be interested to know whether you were ever warned that this kind of behavior could lead to termination. If you were not, it may be helpful to focus on that.
Please keep in mind that you have the right to be represented at the hearing. While the Avvo Q&A page is a useful tool to gather information, it should not replace the personalized advice that an attorney can give you.
The California Unemployment Insurance Appeals Board has a short video available on its website (linked below) that provides a good summary of what to expect. I recommend watching it two or three times before an appeal hearing.
I wish you luck.
Generally the administrative law judges are favorable to the employee. I do not have enough information regarding the alleg misconduct, but generally the judges look for some prior warnings or a clear written policy that is violated. You should look at the EDD site for the decisions that apply to this type of discharge. Credibility will be important in your case since it will be your word agains the other co-worker that you had used the word. When you testify, be calm and professional. Don't get angry and don't ramble. Answer the specific questions the judge asks you. If you do have any witnesses to the alleged reason for your termination you should bring them or have them available by phone
No one can predict your chance of success at the unemployment hearing, however, generally, if you are fired, your employer must show that you are not eligible to receive benefits. That stacks the cards a little bit more in your favor.
You certainly should appeal your unemployment decision, and make sure you appeal on time. You may also want to hire an attorney to assist you in your appeal.
This answer is provided for guidance only. DO NOT rely on it as legal advice. We DO NOT have an attorney-client relationship. You should contact an attorney in your area for a one-on-one consultation before pursuing any action or making any decisions.