Why do the Noble Truths talk about 'craving', instead of about 'attachment'?

Further to [these comments](https://buddhism.stackexchange.com/questions/3545/if-theres-nobody-to-get-enlightened-why-bother/3550?noredirect=1#comment29427_3550) , why do the Noble Truths talk about 'craving', specifically, instead of about 'attachment'? Wouldn't they make as much sense, or even make more sense, if they identified attachment rather than craving as a condition for the types of suffering which are mentioned in the first noble truth?