It is a well-known proverb that is centuries old [1]: it's essentially a canonical way of refering to the concept of something small having big consequences.

Proverbs are often contrived (e.g., "Those who live in glass houses should not throw stones" - who lives in a glass house?).

[1]: https://en.wikipedia.org/wiki/For_Want_of_a_Nail

I hate everything about this, thank you for sharing the context