>> I just don't like relying too much on other people's code.
That may work in some specific cases, but there are tons of reasons to rely on existing libraries over creating your own.
This is especially true of the standard library (part of which in C++ is referred to as the STL). The interface is standardized, so you can be reasonably sure your code will work for a long time on any platform. This also means that most other developers familiar with the language can understand what the code is doing because the library is part of the language. For your own library, it is almost assured that a developer new to the code will have to learn your API from scratch.
The standard library implementations are thoroughly tested because so many people use them. This contrasts with your own library that gets far less testing and will almost always have far more bugs. In some cases you can optimize library functionality for specific tasks you need, but the standard library implementations have all been highly optimized as well, and in many cases this will still be better than your own.
It seems to be a natural tendency to want to write your own solution rather than search for an existing one, but in the end the effort is much greater and the reward is smaller if you do. This is true even for non-standard libraries. In some cases you will find that there are no widely available and tested libraries for a specific task, and in those cases writing your own makes sense.
Your line probably stops at the C standard library. If you are programming in C++, though, that line should at least extend to the C++ standard library, and probably a lot further.