Why are animal births not taken as seriously as human births?
Our heads are bigger.

There's some debate on the issue, but in essence, human brains, and therefore heads, are very large relative to our body size.  This is handy for all the intelligent things we like to do, but can be rather painful during birth.  Because we walk upright, the size of a newborn's head is actually a non-trivial fact during the birthing process.  There are two major implications.

The first is that human birth hurts.  You can watch the birth of other animals and they seem to brush it off, but for humans, forcing that huge head through a relatively small birth canal is difficult.  Evolution has (supposedly) limited the size of the hips because, while that would allow an easier birthing process, it would negatively impact our ability to walk.  As such, it has to hurt.

Secondly, in order to make the process easier, humans rotate during birth.  The end result is that, unlike even other closely related primates, humans come out backward in a way that is very difficult for a birthing female to attend to.  This almost requires having another person or two on hand to help out.  This would, of course, be a huge reinforcement for social connections.

A few books I know of touch on this.  Up From Dragons deals with the brain size/hip size issue and The Invisible Sex talks about rotation during the birthing process and the social implications.