You can think of falsehood as false with a room built around it. The ending -hood is the one in childhood and neighbourhood: it takes a quality and holds it still so you can talk about it. So the picture underneath the word is simply the state of not being true. From there the word moves outward twice. Put that state inside one sentence and you get a falsehood, a single claim you can count. Put it inside a person's habits and you get falsehood, lying as a way of behaving.
From the word’s history
The source gives Middle English falshede, from false + -hede, equivalent to false + -hood, which lines up exactly with the state-of-being-false reading.
來源記載它來自中古英文 falshede，由 false 加上 -hede（即今天的 -hood）組成。這正好對上「假的那個狀態」這個讀法。
Wiktionary (kaikki extract, source_ref kaikki:3f6f69a190036ae4:586457072): From Middle English falshede, from false + -hede, equivalent to false + -hood.
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