"lynching" has a very well-established racial subtext in the US... I'm sure this person didn't intend it that way, but she pointed it out and he apologized, all of which seems completely reasonable.
well... he used the word innocently, then she pointed it out she was offended and he apologized for her misunderstanding him... yes, that was reasonable (to an extent). But then, not willing to let it be, she continued to throw race in his face... leaving him not much choice but to continue to defend himself. That is pretty far out there to me.