From everything I've seen, it's a combination of practical and historical reasons. The (mostly) historical reason is that CPython 1.0 was released in 1989. At that time, C was just recently standardized. C++ was almost unknown and decidedly non-portable, because almost nobody had a C++ compiler.
Although C++ is much more widespread and easily available today, it would still take a fair amount of work to rewrite CPython into the subset of C that's compatible with C++. By itself, that work would provide little or no real benefit.
It's a bit like Joel's blog post about starting over and doing a complete rewrite being the worst mistake a software company can make. I'd counter that by pointing to Microsoft's conversion from the Windows 3.0 core to the Windows NT core, and Apple's conversion from MacOS 9 to Mac OS/X. Neither one killed the company -- but both were definitely large, expensive, long-term projects. Both also point to something that's crucial to success: maintaining both code bases for long enough that (most) users can switch to the new code base at their leisure, based on (at least perceived) benefits.
For a development team the size of Python's, however, that kind of change is much more difficult. Even the change from Python 2 to 3 has taken quite a bit of work, and required a similar overlap. At least in that case, however, there are direct benefits to the changes, which rewriting into C++ (by itself) wouldn't (at least immediately) provide.
Linus Torvalds's rant against C++ was brought up, so I'll mention that as well. Nothing I've seen from Guido indicates that he has that sort of strong, negative feelings toward C++. About the worst I've seen him say is that teaching C++ is often a disaster -- but he immediately went on to say that this is largely because the teachers didn't/don't know C++.
I also think that while it's possible to convert a lot of C code to C++ with relative ease, that getting much real advantage from C++ requires not only quite a bit more rewriting than that, but also requires substantial re-education of most developers involved. Most well-written C++ is substantially different from well-written C to do the same things. It's not just a matter of changing
cout, by any stretch of the imagination.