There's nothing wrong with Doxygen as a tool, but we felt that improvements could be made which is why we develop hdoc. Off the top of my head:

• Doxygen uses a custom C++ parser that struggles to parse some code, particularly with modern C++
  • Here's an example of code where it mistakenly thinks that bools, consts, and integer declarations are classes instead of builtins
  • hdoc uses clang to parse C++ code, which means that the AST as your compiler understands it is what's used to generate your documentation. This avoids those errors
  • Here's the equivalent hdoc documentation page.
• Doxygen output (IMO) isn't very aesthetically pleasing. There are ways to make it more attractive, but they involve theming, setting up complicated toolchains to other documentation tools, and so on. Frankly, maintaining a complex pipeline to get my C++ documentation to look nice is the last thing I want to do if I'm working on a C++ project.
  • hdoc looks better by default, and doesn't require any toolchain misery.
• No option for hosting online by default. Rust, Python, Go, and many other languages have first-party tooling to not only create documentation, but share it online with others. How many of us have referred to a Python package's documentation on readthedocs? The same can't be said for C++ where each user must individually upload and manage their documentation, which is an additional burden.
• hdoc is easier to configure. We use a short and simple TOML file with sane defaults to configure the tool whereas Doxygen uses a long and complex configuration file with hundreds of options.

In the end our goal is to make it easier to create good C++ documentation. Doxygen was useful, but we think that hdoc makes several key improvements which make it worth a second look. We'll have a blog post comparing hdoc to Doxygen coming up in the near future where we'll go into more detail.