I have recently been accused by someone of stealing their idea and doing the work required. In fact they had come to me to do, let's say, a literature review because they didn't have the expertise to do one themselves. They gave me an umbrella topic and told me to figure the rest out. I ran with it and narrowed down the topic to a specific research question. Step by step I made sure to keep the person looped in and updated on my progress, as well as answered their questions (such as: what is the research question? What does this mean? What is the point of doing this review?). When it came time to move it forward, the person bailed and said they were too busy to continue.
A year later, I nudged them again as I wanted to finish it off and said I have other resources now (ask a student to do some data validation) to help complete the next step so we could start writing. The person agreed and we finally started to talk about authorship. They asked what I wanted, I said first as I had done a major part of the work. They also needed a first so I counter suggested we do first co authors as it had requires/requires both of our efforts. They were extremely reluctant, saying that I had stolen their idea and that it was wrong for me to do the work when they didn't have the time, and suddenly say that I deserved first because I had done the work but they also needed me to teach them step by step on how to do the lit review.
I feel that I have not been deceitful by hiding information or falsely claiming authorship away from this person. I believe it was a joint effort although I'm not sure what the norm is. What does actually constitute as idea stealing? Did I overstep by asking to be recognised as an equal contributor?