I don't oppose first cousin marriages, I think there is a reason they are ALLOWED in Islam...
what i do oppose is when families only marry their childern to first cousins or other close cousins, generations after generations...its followed like a strict rule that none of their children, are going to marry out side family...
marrying a non-cousin or out of family is considered a big tabooo in a lot of families in pakistan... I think there's a reason why Islam doesn't anywhere (from any hadees, sunnat, quran verses) advocate this type of cousin/family marriages generation after generation...
it creates a lot of problems (not just genetics/health related problems as others have pointed out, but also many girls or boys don't end up getting good rishtas, some (shockingly) in pakistan remain unmarried, because they couldn't find a compatible (interms of age) cousin to marry...
as far as genetics go... if cousin marriages happen a few times, or once ina while in a family, its pretty ok... the risks are not significant at all...
however imagine, if your grandparents were first cousins, your parents were first cousins, you and your husband first cousins or close cousins, and your child is also going to marry a first cousin or a close cousin....if u continue down this line , then yes, genetics does become an issue because there is no new genes being brought in and mixed with the family's gene pool...
for my kids, if they wanna marry a first cousin, i would gladly give my blessing... because my grandparents were not first cousins (i dont even think they were distant relatives but not sure), my parents were not related at all(2 completely different families), my husband and i are not related (completely different families), so if a cousin marriage does end up happening after a few generations its fine...
Islam doesn't Prohibit it, its perfectly allowed...but Islam also doesn't Specifically select or advocate it as the "first" or "best" or "only" choice either... and we have to keep both these things in mind