A year or 2 ago, my sister narrated this story to me that one of her ex-colleagues along with 2 others were arguing with them that you don’t say Assalam-o-Alaikum when you meet another Muslim, you say Adaab. According to them, it was the right way of greeting another Muslim & Assalam-o-Alaikum is not a proper way of greeting. They all kept on wrangling forever.
A person needs to read Surah Adh-Dhariyat & you may get the answer.
Has the story reached you, of the honoured guests [3 angels; Jibrail (Gabriel) along with another 2] of Ibrahim (Abraham)?
When they came in to him & said: “Salaam (peace be upon you)!” He answered: “Salaam (peace be upon you),” & said: “You are a people unknown to me.”
Surah Adh-Dhariyat [24, 25]
These angels went to inform Hazrat Ibrahim & his old wife about the birth of a son.
The point is that even at that time when people used to meet each other, that is how they greeted.
George Bernard Shaw very says, ‘Religion is such a great thing that when I meet really religious people we are friends at once, no matter what name we give to the divine will that made us & moves us.”
And here people argue as to what is the right way to greet or wish others. Or should I say those people were basically trying to prove that the other sect is totally wrong. Yeah we are badly divided.
And we all must have encountered people who don’t respond when you say Salaam to them. I think even when your enemy greets you, you must greet him back.
I also think it’s the wish that matters & not how people wish each other. We, humans, are supposed to make this world a better place, but we have created all sorts of unnecessary arguments.