I have learned, and seen in practice, that we don't invite people to a b'rit milah directly but rather just announce a date and place. The reason, according to this answer citing Rema Yoreh Deah 265:12, is that it would be bad to decline an invitation but if you weren't invited, you can choose to not attend.
I understand that b'rit milah is an important mitzvah and worthy of celebration, but why, more specifically, is it bad to decline an invitation to one? We don't seem to have this problem with other s'machot, like weddings. (Or, at least, I couldn't find any "not really an invitation" wordings for weddings via Google.)