Well, there is genetic danger depending on which chromosomes you and your cousin share. Genes are actually a bit more random, it's easy to say "you have half your mom's DNA, and she has half her mom's DNA, ergo you have one quarter your grandmom's DNA". In reality, you inherit 23 chromosomes from your mom, but it's a coin flip for each chromosome as to whether that one came from your grandma or grandpa. Flip a coin 23 times and count how many times you get heads, could be 12, could be 8. It's very common to get 10 chromosomes from grandma, it would not be unusual to get 16, rarely you could get 3. Getting absolutely none has a chance of 1 in 8 million, which makes it incredibly unlikely but hey, that means there are 1000 people out there with no (nuclear) DNA from their maternal grandmother. A cousin is expected to 1/8th of your DNA, but it could be a bit more or less. So you don't know just how much danger there is in first cousins. Best to, you know, date outside the family instead of simply hoping the nasty genes will breed themselves out.
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@wumpus
Well, there is genetic danger depending on which chromosomes you and your cousin share. Genes are actually a bit more random, it's easy to say "you have half your mom's DNA, and she has half her mom's DNA, ergo you have one quarter your grandmom's DNA". In reality, you inherit 23 chromosomes from your mom, but it's a coin flip for each chromosome as to whether that one came from your grandma or grandpa. Flip a coin 23 times and count how many times you get heads, could be 12, could be 8. It's very common to get 10 chromosomes from grandma, it would not be unusual to get 16, rarely you could get 3. Getting absolutely none has a chance of 1 in 8 million, which makes it incredibly unlikely but hey, that means there are 1000 people out there with no (nuclear) DNA from their maternal grandmother. A cousin is expected to 1/8th of your DNA, but it could be a bit more or less. So you don't know just how much danger there is in first cousins. Best to, you know, date outside the family instead of simply hoping the nasty genes will breed themselves out.