Rosh Hashana is part of עשרת ימי תשובה. So why is there not a mention of sin on R"H?
If your relationship with your wife is based on 1] what you do wrong and 2] apologizing for it, then you are in a bad place ח"ו.... A healthy relationship is based on LOVE.
Teshuva is not about sin. Sin is an impediment to being close to Hashem. We have to deal with our sins to remove the impediments to our relationship to Hashem.
First, the bracha of הרוצה בתשובה without a mention of sin and only then - סלח לנו and dealing with sin [שפ"א].
Teshuva is Ahava and Dveykus. ושבת עד השם - returning to our source. Loving and being one with Hashem.
THAT is Rosh Hashana. We put everything aside, return to our source and crown Hashem. We blow the shofar to bring us back to the ויפח באפיו נשמת חיים of Hashem's blowing our G-dly Neshama inside of us. When we are connected to our Neshama, we are connected to Hashem.
THEN we spend the next 8 days dealing with our sins.
"חקרנו על גדר התשובה ... קירבה לה' מריחוק החטא" [מבי"ט בית אלהים פ"א]
[Note: This is a short thought and of course in no way encompasses the infinite depth of Teshuva].
