In Islam, all scholars seem to agree that shaving off the beard is prohibited(Haram) and some say at least part of it should be kept.
What is the reasoning for this rule?
Edit: It seems from the comments that you are inquiring about the reason or wisdom behind growing the beard. You need to update your question accordingly.
My original answer is mentioned below. Two similar ahadith with slightly different wordings and chains tell us the reason (emphasis mine):
Ibn Umar said: The Messenger of Allah (may peace be opon him) said: Act against the polytheists, trim closely the moustache and grow beard. (Saheeh Muslim)
Abu Huraira reported: The Messenger of Allah (may peace be upon him) said: Trim closely the moustache, and grow beard, and thus act against the fire-worshippers. (Saheeh Muslim)
The explanation of these from 50,000 feet: Islam came to protect five things. Among them is the protection of deen (religion) itself.
Based on this goal, you see many rulings in Islam that pertain to the deen, and that specifically mention other nations (Christians, Jews, and polytheists). We are frequently referred to them and told not to imitate them, thus dissolving our religion.
The two ahadith quoted above in Saheeh Muslim show that, in this case, we know that the command to grow beards is for safeguarding of the religion -- to distinguish ourselves from other nations and past religions.
The ruling on the beard is quite clear. Rasulullah said:
Trim the mustache and grow the beard. (Bukhari and Muslim)
Based on this hadith, and other proofs (including the practice of the companions), scholars derive the ruling that growing a beard is fard.
The technical definition of fard is:
Any action which you are rewarded for doing, and punishable for not doing. (Usool Ul-Fiqh Principle)
This is something we intuitively understand -- if growing the beard is fard, shaving it is haram.
But anyway, based on this principle, scholars deduce that shaving the beard is haraam, and it's the opposite of growing the beard.
And Allah knows best.