The reason why some people will tell you that learning C prior to C++ is because it teaches you "non-object orientation bad habits".
This is utter bullcrap. Object Orientation is a good thing, but it's not the end-all-be-all that some people make it out to be. Just like a tool isn't the right one for every task, neither are program paradigm (object-orientation, functional programing, procedural, etc).
There are a number of reasons why C is still used in a world where C++ exists. A program written is C is generally faster than one written in C++. A significant number of the programs and open example source code that are out there are in C.
Now, most colleges will teach C++ as one of their introductory languages. My point is that if they're going to teach that to you eventually, why not learn another, just as common, language now, especially being that most of your knowledge will carry over to that training.