Even before that baby pops out, parents are worrying. Will the child be healthy? Will he be smart? Will he have his father's ugly nose? Which crib is the best? What about the 17 strollers at BabiesRUs? And on and on. This is just the tip of the iceberg.
Once born, then the anxiety really sets in. Most parents have no real hands on experience with caring for an infant, especially one this important (this is the survival of your genes we are talking about). Everything is new and every little grunt or poop makes the new parent wonder if everything is alright.
In fact, everything is completely fine for the vast majority of infants. Most infants are perfectly healthy. Sure some will have issues, but statistically you are much more likely to have a healthy child than not. Yet, most parents dwell on that very small chance that something is wrong or going to go wrong. It is akin to the guy who is convinced he is going to get rich by playing the lottery. Most of us realize that the chances of winning the lottery are minuscule so we go to work each day. Yet, most parents are convinced that they are going to win the unhealthy child lottery. So they buy tickets daily, even multiple times a day. They are so convinced that they have won they rush to the emergency room because the baby has not had a bowel movement in a day. Fortunately, most of you are not going to win the unhealthy child lottery. That is just how it works.
Don't get me wrong, bad things can happen, but the vast majority of these bad things are not preventable, and, certainly, worrying that they might happen does not decrease the likelihood of them happening. Statistically, bad things are much less likely than most parents believe, and realizing that statistics are in your favor is a very good starting point for quelling parental anxiety.