If that's how the whole world has worked until now, then the fault must be within me

Human civilization worked without electricity for thousands of years. That doesn't make the lightbulb a mistake.

The norms of other eras and other societies do not apply to the context in which you and I live. If you need absolute proof that "girls need to get married and pop out babies" is absolutely untrue now, look no further than this graph: http://people.eku.edu/ritchisong/pophistory.gif

For most societies throughout most of human history, making more people was one of the most valuable services a person could perform; unfortunately for women, they were the only ones who could do it. Fortunately for women, population is no longer a particularly scarce resource, so that burdensome activity no longer has nearly as much value, which allows women with other interests to do pretty much anything else.

Frankly, our society has more women than we need who want to get married and pop out babies. I can't see a rational case for encouraging anyone who doesn't want that to start it up - have you really heard such an argument, or have you just received intense social pressure with no actual logic behind it?