Some people are highly strung. One word can trigger them. Maybe even one look.Some are predisposed against certain people or questions.
I asked a person "Are You Jewish?"
They responded "That is an insult!"
I asked "If someone asked you "Are you an Accountant? - would that insult you?"
He responded "Yes." I guess he wouldn't like to be an accountant.
(Come to think of it Saying "Being Jewish is an Insult" is an Insult - but I let it slide.)
Some people were hurt in the past. Some have a disposition against you, because they heard something bad against you. So they act with an angry disposition towards you.
Rabbi Yitzi Greenman, a Fund-Raiser for Aish HaTorah tells of a story of a Wealthy individual who had an angry disposition towards Orthodox Jews. He was patient and persistant and eventually turned around that disposition to eventually get the man to give a sizeable donation.
So whose problem is it, if someone is angry at you? If you really hurt the other person - or perhaps you angered them - it would make sense to make amends - if the relationship is worth it. (In cases of marital / couple relationships an Orthodox Rabbi would be proper to consult before returning with a spouse that is abusive)***
But sometimes it's not you. They had a bad day. They listened to "lashon hara" / evil speech about you or your kind. So it is not your fault. Something is wrong with the other person's disposition.
The Torah gives the ultimate response to disarm a person -
"A Soft Answer turns away Wrath." (Shlomo Hamelech / King Solomon in Mishlei / Proverbs 15:1) When someone is angry, the best response is not to stoop to an escalation of anger. The best is to remain in control. A soft answer helps one to both and disarm the angry fellow.
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***Also, in cases of Intermarriage - it would be better to just walk away - because of the Torah law - prohibiting it. The Torah tells us (Devarim 7:3-4) “Don’t marry with them – don’t give your daughter to his son, and don’t take his daughter for your son; lest he should turn your son away from Me, and they will worship other gods...") (The Jewish View of Marriage) (Law on Intermarriage) (Meaning in Mitzvot - Intermarriage) Usually a child of a mixed marriage is confused. They are not sure where they belong. Besides the Torah's reason, It is unfair to the children that may result from such a union. People who start off on the same wavelength, usually have more successful, happy marriages.
