As always, this is my humble perspective based upon my experience, so please make of this what you will. There are also cultural differences (both in terms of people and in terms of institute cultures). But I have seen two broad categories of student projects. The first involves students being given a project. The second involves the student generating their own research program. So, what are the pros and cons of each? Should you push your own agenda?
Supervisor-Developed Research Programs
This involves joining an existing research program and being given a research question, a design, sometimes ethics is done and some/all data are collected. There are a lot of pros to this approach. You can be confident the project will be enough for your study, that the rationale is solid, and you can start right away. These kinds of projects also sometimes means access to more inaccessible samples. You can also be confident that your supervisor can provide a lot of support on the topic. There may even be scope to tailor the project to your interests – add a variable, ask a different question, etc.
But this comes at a cost… This is not your research baby, it is someone else’s. You’re playing babysitter, potentially for years. Are you happy to do this? Are you also happy to forego experiencing some of the difficulties in research?
Self-Developed Research Programs
The solution? Develop your own research program. Negotiate with your supervisor to generate your own research questions within their area of expertise. Choosing your own research project means that this is your research baby. You will almost certainly become attached to it. There is also a higher degree of agency. The precursors to arriving at your own research question also mean reading extremely widely, so not only do you have your own research question, you have a deep and intimate knowledge of both the area of your project, and those areas around it.
But this model comes at a pretty high cost. The anxiety, the uncertainly, the pressure, it is all much higher in this model. Supervision meetings may require you to justify your stance or convince your supervisor of your ideas, which can be daunting. Then there is just the general fear that you won’t be a good research parent to your research baby. That imposter syndrome. There can also be a lot of hesitation around making your own decisions and acting on a high level of agency. There is also a risk that your project, no matter how well you argue it, might have flaws or problems that neither you nor your supervisor saw. So the big question here is whether you can work in situations where there is a high level of uncertainty and where you’re required to make decisions?
Personally, I don’t think one approach is superior to another, but rather it is about what approach fits what student-supervisor combinations better. For supervisors, perhaps consider it on a student-by-student basis. For students, consider what you want out of your studies.