Thesis: supervisor's project or my project?
My impression is that a PhD student should be able to determine what projects to work on and to include in the thesis. Obviously I am happy to do some side projects to keep my supervisor happy, but I am hoping that I should be able to decide what I want to work on without offending my supervisor.


In an ideal world, yes. In reality, there are practicalities to consider:


At least here in Europe the biggest factor is what the grant that pays for you says. If you are, for instance, funded via an H2020 project, you are most certainly not free to decide what you want to work on. Your money comes with a clear "description of work", and substantial deviations from this work plan need to be justified. Other grants may be less (or, in case of industrial funding, even more) strict, but there is certainly no universal rule that as a PhD student you should be free to work on whatever.
Another factor is the strategic research plan of your advisor. Your advisor has, or at least should have, a long-term plan, and if your project does not fit in with the plan, your project may be, speaking bluntly, a waste of time and money for him, even if it is an otherwise nice project.
There is also the problem that your advisor also requires some competency in your project, both to help you when you are stuck and to evaluate your progress and final dissertation. Many advisors will be unwilling to supervise students on research attempts that are too far outside their core expertise (usually also in combination with the previous point, that those are often simply not very valuable to their long-term goals).
Finally, your advisor may also be wary that the project may not be academically promising enough. I have seen often that younger researchers tend to confuse projects that are "interesting to work on" with those that are "likely to lead to interesting results". You should at least consider why your advisor is "not interested in your results", and ask yourself the question whether other senior academics will feel the same.


Of course this does not mean that you always need to slave for your advisor and should bury all ambitions of developing projects on your own. In practice, the best PhD students juggle their own interests with the interests of their advisor.