A lot of apps (old-timey Windows apps, for example) have this philosophy, leading them to reinvent things like crypto and image decoding. Naturally, this leads to tons of bugs, including security bugs. I would revise this to: Don't bring in more code than you need. But if the choice is between writing something yourself and using someone else's well-tested, heavily-used library, always go for the latter.
There's an important kind of compromise that isn't discussed as often: using an external library but behind an interface of your own design, an "anti corruption layer". If the external dependency is limited to one small bridge in your application, then it's so much easier to see what parts of the dependency you actually depend on, to upgrade the dependency when its API inevitably changes, to replace it entirely if it…
Mycode -> facade -> library
Navigating code becomes more cumbersome and stack traces longer. I do like this approach too but it isn't free.