I've never used the month view, but I just tested it and tapping on the day in month view takes me to whatever calendar view I was in previous to be in month view. If I was in agenda previous to month I go to agenda, if in day view I go back to day view. So, being in month view and tapping a day doesn't always necessarily take you to agenda view. Just for information as I wasn't aware of how this process worked.
I wasn't able to find a way to get "new event" to come up just by tapping the day when in calendar view.