Playing devils advocate here re: “you’ve got a case”. First you need to check some things out. Is your state a right-to-work state? Is your position unionized? are you a new employee on probation?
All those questions about “did they tell you about a problem and give you time to do corrective action” make sense ONLY if you don’t work in a unionized environment, were NOT a new employee on probation and do not live in a right to work state.
In a “right to work state”, unless you are governed by a union contract or a personnel policy from the company that says otherwise, an employer can discharge you at any time ** without ** stating a reason. Now, if you file for unemployment benefits, the employer must show sufficient cause for firing to the UE administration before or the employee can collect unemployment.
you don’t state how long you were working there. If it was only a short time, you may still have been on new employee probation (a frequent thing). If you were, employers can let you go for something as vague as “things aren’t working out”.
Now. what to do? well, you may check in with your local Civil Rights office (of your state government) to see if there was a sexual basis (the fact that you were the only female is suspicious, but not proof). File for unemployment compensation. You are more likely to get a specific reason stated.
You mentioned one customer complaint but said “it wasn’t true”. Are you saying the customer DIDN’T complain? or that you weren’t sarcastic? If the former, then something is fishy. If the later, then that’s a problem. If you’re working in customer service and a customer says you were rude, sarcastic whatever, the fact you didn’t INTEND to be rude sarcastic or whatever is not necessarily germane to the issue. Whatever you said or did apparently was open to that interpretation to the customer. You’re better off looking at that incident and seeing if you MAY have said something that could have been misinterpreted and taking the tactic of "I’m sorry that you felt I was being… "
And, as a general rule of thumb, discussions of how badly other employees act is not relevant to a discussion about what your behavior is. I know it seems unfair (they act worse with the bit bosses than I do), but if I’m talking to an employee about their conduct, I will NOT entertain comments about “yea, but Joe acts worse”.
Make this a learning experience no matter what the outcome is. New employees actions will always be looked at more closely than some one who has demonstrated a long history. It is my belief that the general “not getting along with others” is the second most reason for folks getting fired. Employers are generally willing to train at tasks, but if they have complaints from coworkers, customers, supervisors etc. nah. And they have told you they’ve had complaints from customers and supervisors. You deny them. But, again, are you saying the person didn’t complain or were incorrect?
When I teach folks how to get along with supervisors, I tell them that, as a supervisor, I expect to need to tell people (at least once) how to do something right. HOW they react is important to me. If they get defensive and start saying stuff like “well, this is how I’ve always done it” or “But this is a better way” or “well, no one TOLD me to do it that way”, I find it annoying and not particularly helpful. If they over compensate with a 10 minute apology, I’m also not happy. What I’m looking for (and most supervisors) is for you to say “Ok, will do” and maybe “thanks” For some one to make what should be a 2 minute exchange into a long drawn out defense of what they were doing (at the point when I’m pretty much telling them to NOT do that) is not only pointless, but counter productive, and YES, falls into the case of “not taking correction well”
In the exit interview, try and find out as much as possible about how they expected you to handle things. Please understand that I’m sympathetic to you in this situation. I’m not trying to say that you did any of the above actions. Those were just examples of things I’ve seen folks do that got them fired. I’m just trying to offer some courses of action that will be of benefit to you in the future. The fact that these people apparently found you difficult to work with does NOT mean that you’re a bad person or even in general “difficult to work with”. Hopefully, you’ll be able to learn from this and prosper in the future. Best of luck to you.