Why will God open a fountain for the house of David and Jerusalem in Zechariah 13:1?
The prophecy states the fountain is opened for sin and uncleanness. In that day, when the Lord establishes His kingdom and fulfills Israel's promises, God will cleanse and forgive the house of David and Jerusalem's inhabitants, bringing them into the glory of the kingdom.
The context connects this to Israel's near-term rejection and falling away from all her prospects, yet in the long term God will still fulfill all the sign aspects of His dealing with Israel. Zechariah 13:1 is prophecy: “In that day” points to when the Lord finally sets up His kingdom and Israel has all the promises fulfilled. The fountain is opened to the house of David and to the inhabitants of Jerusalem for sin and uncleanness; God will cleanse them, forgive them, and they will come into all the glory of the kingdom. As yet, however, they remain in spiritual blindness.
In that day there shall be a fountain opened to the house of David and to the inhabitants of Jerusalem for sin and for uncleanness.