I stand in the presence of God, and I have been sent to speak to you and to tell you this good news. And now you will be silent and not able to speak until the day this happens, because you did not believe my words, which will come true at their proper time. Even more, its dangerous to speak against them. You shall have to be mute until these things come to pass. Gabriel rendered Zechariah mute not in punishment for his unbelief but rather to prevent his unbelief from speaking against God's will.
Words are powerful.
Zechariah learnt this the hard way. John the Baptist must have been told all this by his parents. When he eventually emerged in the wilderness his voice was the the voice of God speaking in the wilderness. His voice filled people's heart with hope and joy. His voice caused a wilderness to vanish.