Original picture: Knowledge sharing (cropped), by Ansonlobo, CC By-SA 4.0
There are multiple reasons why you would not want share research data you've worked on, and the most obvious might just be you don't know why you should. Here are some arguments for your consideration.
A new research output
Open datasets are a new kind of citable output which adds up to your articles and books. When your research didn't achieve the results you expected, the dataset itself still holds some value. And when it did, imagine how valuable the dataset could be for your CV!
It will get you more citations
What's more, it turns out opening your dataset leads to more citations of the articles based on it. Research repeatedly showed such an effect even after considering alternative explanations.
Discover new ways your data can be used
Just when you think you've answered every question you could have about your dataset, someone from a different field or specialisation might just think of a different way to exploit it, which could in turn inspire you for future research.
Shared data = better teaching opportunities
Students like working on actual data rather than endless theory. Why not provide your colleagues and students with some data they can use to learn about the research process?
Access for development
Many researchers at the Institute work on data collected in developing countries, where universities don't have the same research funding options. It is only fair to give them similar access to data about local issues.
Public money, public research
Research at the Geneva Graduate Institute is directly or indirectly funded by public institutions: the SNSF and ERC pay for specific projects, while the Swiss Confederation and the State of Geneva contribute, among others, to the general functioning of the Institute.
We should make sure that research allowed by taxes becomes available to the public. Just because someone is not a researcher does not mean that they should be denied the opportunity when they express interest in your research.
Saving on future costs
This also means that any data should not have to be collected and paid for twice. Saving on that kind of budget means that more projects can be funded by the agencies.
Scientific research is facing a replication crisis. One of the base principles of science is that experiences should be reproducible, which too many actually fail. Opening data allows others to understand what you've done, find possible errors and suggest ways to improve your research.
Data repositories are better suited to long-term data conservation than Dropbox or your personal computer. The operations involved in preparing your data for sharing will also improve its conservation and usability for years to come.