Your second paragraph shows that you didn't understand the chain of events. Let me try and explain:
1. The tutor advised us they only had Thursday available. (We agreed Thursday evening with the tutor in November, even though we knew our daughter had activities that day)
2. We moved these activities to Friday (to free up Thursday and accomodate the tutor) and paid in advance (full term) for these activites.
3. Two days before my daughter was due to start (in January) my wife gave a courtesy call to the tutor and he advised us they only had Friday available, as they moved someone else to Thursday into our agreed slot because they were with them already for a period of time.
You also state the tutor, 'having offered to try and re-arrange' their schedule, which was also our understanding, as we were advised the same. The tutor said on Wednesday he would speak to the parents on Thursday evening when they attended his house. We actually got a call just after 14:00 on Thursday afternoon so the conversation with other parents obviously never took place. My wife also still has the message on her mobile phone with the tutor stating ' I do not want your daughter to come here for tutoring' which I would gladly download and play (if the facility was available), which is a bit stronger then, 'Sorry we are unable to find a timeslot for your daughter', or as you say 'Having offered to try and re-arrange their schedule'.
I do understand that you have had a great experience with this tutor as probably many other people also have, hence they have '34' pupils currently being tutored. We ourselves also went to this tutor as we had a fantastic recommendation from close friends of ours. I suppose the point I'm trying to make is that the tutor clearly made a mistake but unfortunately my daughter is now suffering because of this. We all make mistakes, no-one is infallable but instead of accepting it was their mistake, we've been dropped like a stone because of it. I believe my wife had every right to question their professionalism due to the way we were treated, I'm sure anyone who experienced this would agree.
I believe a forum like this is setup for people to share experiences and give an objective overview of peoples experiences. You are correct when you state there are 'two sides to every story' and I'm sure that a lot of people who have children tutored by these people will give really positive feedback on their experiences, including our friends who gave us the recommendation. Unfortunately for the way we were treated, we can't.