I've been involved in a collaboration project for the past year or so (the collaborator was the one who approached me and they were leading the project), the problem is that the progress from the collaborator side was slow and sometimes clumsy (they would often call for meetings without all things figured out, they would be late in meetings, talk on the phone during meetings and would act as if I had to do part of the project for them [this specific part is already published, so I offered to train the collaborator instead of repeating my whole project, but they refused to learn and said that I should be the one running the experiments since it was my expertise]).
Since I'm at the end of my studies and am managing 2 completely different projects at the same time, my supervisor thought it was best to call off this collaboration. I wasn't too keen on doing so because I knew it would look bad on me, but my supervisor thought it was for the best and also said that they would sort things out with the collaborator.
Turns out that my supervisor corresponded to the collaborator saying that I did not want to continue on the project because I was too busy at the moment (which is true, but not a great way of parting ways). Needless to say, I was embarrassed beyond words, and am feeling like this is going to taint my reputation with the other group that I was working with.
How bad is this situation gonna look for me, professionally? Is it normal in academia to pull out contributions from projects that one feels that is most likely going nowhere? Was my judgement in regards to the attitudes of the collaborator unfair?