Women used to get married to have babies because they needed to get married to have babies. Today women don't need to get married, they can be a working single mum, in most western countries they may also choose to raise their child through government benefits which are much higher than they used to be, and there is no longer any social stigma to being a single mum. At the same time, lower standards of living mean that one paycheck cannot usually give a family a decent standard of living, so the appeal of getting married to be a stay at home wife (which may not be everyone's cup of tea but will obviously appeal to some) is largely gone.
I think it is those reasons, not the selfishness of generation Y, which are mostly responsible for less people getting married.
"Today women don't need to get married, they can be a working single mum, in most western countries they may also choose to raise their child through government benefits which are much higher than they used to be, and there is no longer any social stigma to being a single mum."
This has been proven to be detrimental to the development of children, having both parents is important. This is another perspective of selfishness, at the point that you are having kids you should be thinking about their welfare, not about whether it's acceptable or not. Also, being a single mom means you're going to have to leave your kids to work, right? Meaning they get even less direct interaction with their parents. Finally, planning to use government benefits to support your kids is insanely irresponsible. You should not have kids that you cannot personally support.