By "why" I mean: what were the stated intentions of the namers? More generally, how did the theme of agricultural terminology in algebraic geometry come about?
Tom Lovering has some great notes about sheaves where he explains this. It's essentially what they've told you above. You can find them here: https://tlovering.wordpress.com/2011/04/17/sheaf-theory-essay/
Let me make a few additional comments about some ideas I find rather amusing. The words bundle, as in vector/principal/fibre bundle, and sheaf are both used for the same reason: they denote some sort of packing of stuff. You could argue that this is rather unfortunate, since every bundle has an associated sheaf of sections, and sometimes you can build bundles from sheaves.
This confusion is not exclusive to English. In Spanish, and more particularly in some places of South America (AFAIK), they use the same word ("haz") to refer to bundles and sheaves! Just imagine! Everywhere else I can think about the word "haz" is reserved for bundles and the word "gavilla" is used for sheaves. Both these words are of agricultural origin and denote the same concept as in English: a grouping or packing of things.
One last remark: Funnily enough the Spanish word fasces seems to be directly related to the French faisceaux and the Portuguese faisceau. However, I've never seen it used in a mathematical context. However, if my hypothesis is true and all these words have the same origin, all of them would be directly related to a certain "form of radical authoritarian ultranationalism". (Wikipedia quote).