I also agree to avoid adding complexity through unnecessary dependencies.
> if a library is popular, it contains huge amounts of code that just isn't relevant to your use case.
It is true that many libraries do contain such code, whether or not they have dependencies. For example, SQLite does not have any dependencies but does have code that is not necessarily relevant to your use. However, some programs (including SQLite) have conditional compilation; that sometimes helps, but in many cases it is not suitable, since it is still the same program and conditional compilation does not change it into an entirely different one which is more suitable for your use.
Also, I find often that programs include some features that I do not want and exclude many others, and existing programs may be difficult to change to do it. So that might be another reason to write my own, too.