That was the "or if you just don't like the idea". I'm not debating whether the choices of an atheist are as valid as those of a theist, they are, but the majority of objections to organ donation would seem to stem from religious views.
You don't need to explain your choices as far as I can tell, all you would need to do is to opt out of the system which will have to be pretty simple "tick no and enter your details to be removed from the register". The opt in is certainly about that level so I see no obvious reason why the opt out would be of any greater complexity. So you can opt out because of religious reasons, because you don't like the idea, because you don't like the presumption, because.... and no one is authority is about to question you for it.