A doorway requires special protection. When it’s open anything can come in and anything can go out. It is the same with new revelations that enter your heart. It needs protection in order for us to receive it, and then it needs protection that it should not get lost. The mezuzah on the right side of the door enables the holiness to enter our homes and the Chanukah lights on the left protect that holiness from being lost.
The Greeks endangered the Jewish people by breaking their doors, physically and spiritually. Physically, they broke the doors to the Beis HaMikdash. Spiritually, they forbade the Jews from observing Shabbos, Rosh Chodesh and bris milah. All three are doorways – Shabbos is the doorway of blessing for the week, Rosh Chodesh is the doorway of blessing for the month, and bris milah is the doorway through which Jews are brought into the world.