Muslims have beards because the Prophet, peace be upon him, on several occasions commanded us to, and we must follow his example without hesitation or shame. He said:
"Be different from the mushrikeen: let your beards grow and trim your moustaches." 
We should not imitate the disbelievers, so letting the beard grow allows us to identify as Muslims on the outside. If we begin to imitate the disbelievers, we will start to imitate their actions and their beliefs and we will go astray.
This is why it is forbidden to shave the beard, because this is contrary to what the Prophet, peace be upon him, said.