If you were still in your initial (probationary) period of employment, your employer can terminate for you for whatever reason they want. Check with the HR policies & procedures, but most organizations do not entertain any official grievance unless the employee is past the probationary period.
I know that it may be a cliche, but "not a good fit" is actually a pretty good reason for not continuing an employment relationship. From the information you have shared, it seems to be applicable in this situation. As a manager, I have terminated staff because of attitude issues or inability to get along with co-workers despite the fact that they had all the requisite competencies and had not had any patient safety issues. Nursing in most environments is a team activity and managers sometimes have to make decisions that support team cohesion/camaraderie.
It's OK. Very few of us (myself included) make it through a career without being fired at least once. When it occurs in your initial period of employment, it can easily be explained as "not a good fit" and not due to performance issues. I know that it may not seem like right now, but (based on my own experience) it can even become a positive influence if you learn from it and move on rather than harboring bitterness that will affect any future positions.
Best of luck to as you move on from this awful experience.