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.
This is pretty much what Rob Pike advocates in Go: "A little copying is better than a little dependency." http://go-proverbs.github.io/
> Clear is better than clever.
> Reflection is never clear.
Of course, everything has its place, even reflection.