I don't get why they restrict the programming languages that can be used. Why can't I just use whatever programming language I please?

This is due to the competition environment running in virtual environments that need to be able to build and run all the entries.

It's not so easy to enable - there are no simple, reasonably automated and secure ways to deploy,run&evaluate solutions developed in/for an arbitrary environment; there are multi-language code-evaluation environments that allow to do this for many but not all languages.

You don't want to run arbitrary binaries; linking of required libraries is an issue in many languages, and you can't install every version of every possible interpreter in the world to support all possible interpreted languages (and their multiple, incompatible versions).

F# is very likely to be added (unless we run into some problems), thanks for your feedback :)

Thanks -- seriously thinking about getting a team going.