It starts a lot sooner than that -- parents set the tone of entitlement and protection from adversity from birth. Watch any parent who shadows their toddler around a park within arms reach and you'll get a sense of how it starts -- it can be very difficult to give a child freedom to explore if it also comes with freedom to get hurt. 

An earlier comment made the interesting point that with lower birthrates, parents have more time invest in each child, and that can easily turn into overprotectiveness. Often, the more kids you have (I  have three), the more you realize your kids will be okay if you're not hovering over them all the time--and that is when they learn to be independent and solve problems on their own. It's not a complete explanation, since obviously parenting styles, individual personalities, and life circumstances are very important, but it may help explain some of it.