Picture a long stick with a sharp point. The ox will not move, so the farmer steps behind it and gives it one poke. The animal does not go because it wants to; it goes because something sharp touched it from behind. That stick is a goad, and to goad is to use it. Later the stick became words, a deadline, or an offer, and the animal became a person. The picture stayed: something pokes from behind, and only then does the one in front move.
From the word’s history
Wiktionary traces goad to Old English gād, the pointed stick itself, and further back to a root carrying the sense of urging on or throwing. So the modern figurative use did not invent the picture; it inherited a real tool.
Wiktionary 記載 goad 來自古英文 gād，本義就是趕牲口的尖棍，再往前的字根帶有「往前趕、投擲」的意思。所以今天「用話刺激人」的比喻，是從一根真實的棍子走過來的，不是後人硬掰出來的畫面。
Wiktionary entry for goad (kaikki extract supplied in this packet, source_ref kaikki:3f6f69a190036ae4:645189833)
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