Looking at this C# code:
byte x = 1;
byte y = 2;
byte z = x + y; // ERROR: Cannot implicitly convert type \'int\' to \'byte\'
The result of
In terms of "why it happens at all" it's because there aren't any operators defined by C# for arithmetic with byte, sbyte, short or ushort, just as others have said. This answer is about why those operators aren't defined.
I believe it's basically for the sake of performance. Processors have native operations to do arithmetic with 32 bits very quickly. Doing the conversion back from the result to a byte automatically could be done, but would result in performance penalties in the case where you don't actually want that behaviour.
I think this is mentioned in one of the annotated C# standards. Looking...
EDIT: Annoyingly, I've now looked through the annotated ECMA C# 2 spec, the annotated MS C# 3 spec and the annotation CLI spec, and none of them mention this as far as I can see. I'm sure I've seen the reason given above, but I'm blowed if I know where. Apologies, reference fans :(