You don't need a master farmer to build a scarecrow - an adept farmer will do just fine. Master farmers (like any other skill) require enough work to reach that level. If you've not yet built the scarecrow, your farmers haven't worked nearly enough to reach master level. If you have too many farmers working on limited food supplies (like the farm), each one will get only a share of the work and will gain skill more slowly than if you dedicate a smaller number of villagers to farming.
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Barbara
Unicorn
Last Day of Work