Rice depends upon specific climatic conditions, and especially hydrological conditions, to grow. Europe simply doesn't have those types of conditions in any plentiful manner. (this map gives you an idea: http://upload.wikimedia.org/wikipedia/commons/1/18/RiceYield.png). Egypt is one of the few places in the Mediterranean with the type of conditions that allow rice to flourish.

As for leavened bread, I am not sure what exactly you are referring to by North East Asia? Are you talking about Siberia? Or Korea/Japan? Because bread certainly was a staple in the later two.

As already posted, the climate has a lot to do with the crops originally cultivated in a certain area. This is one main reason the Europeans didn't develop rice. Another big one is that they simply didn't have the infrastructure for it. As of 221 BCE, China was unified and would stay that way for the majority of the rest of history. Rice requires paddies and highly developed irrigation techniques, requirements that only spring up and survive when there's relative peace and a strong, centralized government willing to make the initial investment in their construction. China had this. The myriad, warring states of Europe did not. Multiple field systems, such as those that dominated Europe from the Roman latifundia to the agricultural revolution of the 17th and 18th centuries, were, in comparison, easier to create, more resilient to periods of upheaval/warfare, and fit the more decentralized Feudal system of Europe.

A great direction to go from this question is to ask what the effects of this difference in staple crops. I won't get into it here, since it wasn't asked, but it's really quite fascinating to see the divergence caused by such an important, yet often overlooked denominator such as a society's main food source. If this is something that interests you, I'd be happy to talk about it more, or recommend the book Civilization and Capitalism by the master, Fernand Braudel, or email you the paper I wrote on the subject. PM me if interested