Women have been giving birth for a very long time - often without men at their side. It really isn't a big deal.
Even though it happens every day, much as it's happened for eons, it's ALWAYS a big deal, because that baby represents possibility.
Men just didn't realize how much of a big deal it was until they started staying in the delivery room and watch the amount of work that goes into it, especially if it's a natural childbirth. Even if you've been to Childbirth preparation classes, you just don't know what it's like until you've been through it.