To begin with, you haven't even defined "hookup culture," much less demonstrated that its prevalence is significant enough to influence birth rates or, further, proven that its influence on birth rates would be negative in the first place.

That said, why assume a nebulous concept like "hookup culture" is causing declining birth rates when a simple google search will reveal plenty of well-studied factors with demonstrated influence on fertility (not to mention far more cultural universality). For reference, some examples include: increased educational attainment among women, increased labor-force participation among women, increased urbanization, increased cost-of-living