There were a bunch of reasons for the choice of C over C++:
1. At the time, we were doing a bunch of stuff with LLVM in the templating language. I'd previously been responsible for trying to integrate LLVM with C++ generated code, and it is painful, mostly because of name mangling and vtable dispatch. Providing a C API sidesteps this entirely, as LLVM can call into C code and use C structs no problem, and once the API is in C there's little reason to make the internals be in C++.
2. We wanted to provide tooling for this templating language, and the easiest way to write tooling is in Python or some other scripting language. It's easier to provide Python etc. bindings with a C API than a C++ API.
3. We'd intended from the start to open-source this. One of the team members had significant open-source experience, and he pointed out that within the open-source community, there are a number of people who basically refuse to use C++ and will instantly disqualify a C++ library. So regardless of whether these people are right, to reach the maximum number of people and prospective projects it should be in C.