I like being able to have complete control over the web interface. I like that it's lightweight, unlike say Gitlab, yet provides a full website. I like that the bug tracker is part of the repo rather than part of a company's proprietary infrastructure.
The biggest advantage, by far, is that it's not Git. I agree that Git is good for a lot of projects. It's an unnecessarily complicated beast for small projects with a couple of collaborators, neither of whom are willing to spend hours dealing with weird commands to handle a repo that got messed up for unknown reasons. Fossil, unlike Git, is version control that others are willing to use.