Shouldn't it vary depending on the number and the gender of the addressee, e.g. 'alayka, 'alayki, 'alaykuma ? But I almost never heard the other variation. Is there a religious or grammatical reason for this, or is it just non-Arab Muslims unfamiliar with Arabic grammar?
I think that it is the lack of knowledge of the people who do not speak the Arabic language and for those who speak it naturally, lack of education.
When addressing 1 person male, it should be said:
While addressing a 1 person female, it should be said:
For example, take the following Hadith
قَالَ أَبُو عَبْدِ اللهِ وَقَالَتْ قَيْلَةُ قَالَ رَجُلٌ السَّلاَمُ عَلَيْكَ يَا رَسُولَ اللهِ، قَالَ وَعَلَيْكَ السَّلاَمُ وَرَحْمَةُ اللهِ
Qayla reported that a mans aid, "Peace be upon you, may Allah bless him and grant him peace." He said, "And peace be upon you and the mercy of Allah."
The same is true when viewing many other hadiths of the same nature. It was never reported from the Sunnah or general Arabic culture about 1 person meeting another 1 person and giving him/her the salutation for the many, just doesn't make sense.
WHY DO MUSLIMS GREET IN PLURAL
As-salāmu ʿalaykum written in Arabic as السَّلَامُ عَلَيْكُمْ is the standard Muslim greeting which means "peace be upon you all" in plural and for all genders even when addressing one person. When I was growing up I heard our elders spoke about the two kiraman katibin كراماً كاتبين which means the "two honourable scribes" who are two unseen angels called Raqib and Atid who sit the right and left shoulders of everyone with the duty to record our good and bad deeds. The Quran refers to them in two places, in 50:16-18 and by name as 'Noble Recorders' in 82:10-12. My understanding is that when we greet one person in plural we are actually greeting that person’s assigned scribes as well – hence we say “peace be upon you all”.
It's in plural because the greeting is directwd to the person and the two angels guarding each one of us, according to the Islamic culture. Me, as an Arabic student and translator, I feel deply embarassed to see that someone decided to judge all Arabic speakers and Muslims as poorly educated without trying to search a bit deeper in the cultural or religious explanation. There are indeed hadith in the sunna regarding the use of the plural and even discouraging the singular, as it is considered the greeting given to the dead.
Muslims say Assalam o Alaikom (al salamo alaikum) even to someone (single) as well as the case or the form of plural?
This can have some reasons for saying Assalamo alaikom (in plural shape) instead of assalamo alaik (which is for the single for of that.
It can be possible to be relevant to some countries cultures.
It can be used as a habit that some or many people use it like that.
It can be relevant for being angel(s) who are always with the human in order to noting good and bad deeds of us. (Therefore we use that with the intention of greeting or saying hello to our parties and the angels as well)
And eventually it is used in order to showing our respect (more respect) to the individuals who we are saying hello to