During every Shemoneh Esrei of mussaf, we pray that the Beis Hamikdash be rebuilt. However, only on Yom Tov do we mention that it was destroyed due to our sins - ומפני חטאינו. On Shabbos, and on Rosh Chodesh, we don't mention this.
However, when Shabbos and Rosh Chodesh coincide, we do mention our sins - ולפי שחטאנו.
If neither Shabbos nor Rosh Chodesh demands a mention of our sins, why does the combination require it?