I suspect it’s to prevent you from using the object before at least the base class constructor has run, ensuring that all the base class members are appropriately initialized. (Variable initializers are executed before the base class constructor, whereas the constructor body is executed after that.)
Will check whether the annotated spec has anything to say about this when I’m next near it…
EDIT: The C# 4 annotated spec doesn’t have any explanation. Just (in 10.5.5.2):
A variable initializer for an instance field cannot reference the instance being created.