Bcoz the Cullens have a vegetarian food diet means they drink animal blood just like the Denali Coven and they are among few of their kind to choose such a diet and as a result have golden brown eyes, the others drink human blood and therefore have red or crimson eyes
vampires..when they are newborn, have red eyes due to the humsn blood still in their bodies. if they choose i diet of human blood their eyes will remain red.
the cullens and also the denali clan, have topaz eyes. this is because they drink the blood of animals- this dilutes the venom in their system (the venom is what gives them the red coloured eyes)giving them the topaz colour
this is how it works:
drink animal blood: gold or brown [cullens and denali coven]
drink human blood: red or crimson [volturi, james's coven etc]
newborn: red because of the human blood from before their change.
hopes this helps!