First, a few evidences to know what we are dealing with:
Allah (SWT) says in the Qur'an:
"He who obeys the Messenger has indeed obeyed Allah." (An-Nisaa 4:80)
"And obey Allah and obey His Messenger." (At-Taghaabun 64:12)
"The reply of the believers when they are summoned to Allah and His Messenger so that he can judge between them, is to say, 'We hear and we obey.' They are the ones who are successful." (An-Noor 24:51)
"Whoever disobeys the Messenger after guidance has been clarified to him, and follows other than the path of the believers, We shall give to him what he deserves and broil him in hell, which is the worst abode." (An-Nisaa 4:115)
"Follow not the whims of those who have no knowledge." (Al-Jaathiyah 45:18)
Rasoolullah (SAW) says:
"Verily, the best guidance is Muhammad's guidance." (Sahih Muslim)
"Whoever imitates a people is but one of them." (Abu Dawood; Hadith Sahih)
Ahaadith pertaining to the command of growing the beard:
"Be different from the Mushrikin (those who worship other than Allah (SWT)); trim your moustaches and save your beards." (Sahih Al-Bukhari and Sahih Muslim)
(In other Sahih narrations it is mentioned in this manner: "trim your moustaches and let alone your beards"; also "lengthen your beards")
"Ten things are fitrah (natural). To cut the moustache and lengthen the beard (are from amongst these ten things)." (Narrated by Hadhrat A'ishah (RA); Sahih Muslim)
An account relating the displeasure of Rasoolullah (SAW) on seeing a beardless person:
Kisra, the Persian Emperor, after tearing off the letter that Rasoolullah (SAW) sent to him, asked his ally Baazaan, the ruler of Yemen, to summon Rasoolullah (SAW). Bazaan dispatched two men to capture Rasoolullah (SAW) [Na'oozubillah]. When they came into his presence, he noticed that they had shaved their beards and grew their moustaches. He hated to look at them and addressing them, he said: "Woe be to you, who told you to do so?" They replied: "Our lord! (referring to Kisra)" Rasoolullah (SAW) then said: "But my Lord, may He be exalted and glorified, has commanded me to leave alone my beard and to trim my moustache." (Narrated by Ibn Jarir; Hadith Hasan)
From the above evidences, it can be agreed upon that the growing of a beard was an explicit command of our beloved Rasoolullah (SAW).
But what about the "It's only a Sunnah not a Farz" argument?
It is a Sunnah, no doubt, but there is a difference between an explicit command and a recommendation. An explicit command of Rasoolullah (SAW) HAS to be obeyed. Why? The aayaat quoted above should suffice as an answer if we are of the opinion that being a Muslim itself does not warrant the obedience of Rasoolullah (SAW). We will all agree that Allah's (SWT) command is Fardh. So, didn't Allah (SWT) ask us to "obey His Messenger"? This goes to say that obeying an explicit command of Rasoolullah (SAW) is commanded by Allah (SWT). Not doing so is going against a command of Allah (SWT).
A practice which Allah's Rasool (SAW) has simply recommended comes under the optional Sunnah. Take for example the sunnah of the Miswaak. Here's a hadith on the virtues of doing Miswaak: "Hadhrat A'ishah (RA) narrates that Rasoolullah (SAW) said, 'Making Miswaak purifies the mouth and is a means of gaining the pleasure of Allah (SWT).' (Mishkat)" Making it a practice of doing Miswaak will earn us Allah's pleasure and will purify our mouth at the same time. Not doing so will deny us these benefits. Similarly, the Sunnah of applying perfume ('Itar) carries great virtue, yet, it is only optional.
Let's look at an example from the life of a Sahaabi (RA) concerning the obligation of keeping the beard:
Upon being asked by a Sahaabi of Rasoolullah (SAW) as to why he always has the hair of his head shaven, Hadhrat Ali (RA) said: "I have heard Rasoolullah (SAW) as saying: 'Impurity exists beneath every strand of hair.' (Mishkat)" Hadhrat Ali (RA) had very thick and dense hair, and therefore, he used to shave it regularly because he feared that growing his hair could hinder the cleansing during ghusul. It is reported that he also had a very dense beard spanning the width of his shoulders and stretching down to his chest. Why did he then not remove his beard to avoid impurity? It only suggests that as an explicit command of Rasoolullah (SAW), it could not be disobeyed.
Also, none of the Sahaabis (RAA) ever had their beards less than a fist-length as stated by Ibn 'Umar (RA).
Furthermore, all the 'Ulamaa of salaf (pious predecessors), including the Four Imams, other great fuqahaa and mujtahids including Imam Ibn Taymiyyah (RA) concluded that growing the beard to a fist-length is waajib (obligatory) and shaving it is haram.