Actual history? I thought they didn’t know what caused the feud, much less that it was a pig. Or at least that’s what I gathered during the 30 seconds it held my attention.
The pig incident was the catalyst. Problems had been building between the two clans for a while.
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I did notice that the Costner character (IIRC) kept referring to the pig as a razorback. However, I don’t think the pig they showed with a notch in its ear was a razorback, unless the term refers to a wider variety of swine.
The first killing was Asa Harmon McCoy some 13 years before the pig incident because he fought on the union side on the civil war.