One explanation is in the rise of women in careers and education.
A woman has roughly 16 years of fertility, from age 14 to 30. At age 30, 10% of couples can't conceive after a year of trying and the numbers get worse after that. Yes, older couples can have kids, but the probability goes way down.
Culturally, having a child before age 18 is assumed to be a bad thing (4 years). Then if the woman has a college education (another 4 years), then goes for an advanced degree (up to 7 years), or wants to establish herself in her career (5 years?), or wants to work off some of the college debt (5 years), the remainder of her fertile years is not enough for population replacement.
It's largely the same for men, at age 22 they may want to start a career and pay off some college debt for several years. Men can father a child at any age, but by and large they tend to marry people roughly their same age.
It's also harder to raise a family in an apartment than in a house, so for both parents it may "make sense" to work for several years to save up for a house.
(Don't take this the wrong way, I personally feel that women should be in colleges and have careers, I'm just pointing out the conflict of interests here.)
It would seem that culture has to change somehow to allow (encourage) couples to have kids earlier, but I'm not sure how that would work given our current economic system.