Why may the right hand sides in Chomsky Hierachy type 1 be larger? I'm shaking my head because of this question, my Prof. didn't explain it. We have linear space limited automata and they have to satisfy for rules a -> b that |a| &lt;= |b|. 

Why?

I would have said, that it's stupid to allow being larger, because we are space limited and still have to produce all words of a language.

Thank you in advance, an answer would mean a lot to me.
It is not allowed to be larger, it has to be larger! If you allow the right side being shorter, you have context sensitive deleting grammars which have the same power as unrestricted grammars, thus leaving the realms of CSL.

The space limitation you mention relates to the automaton concept that is equivalent to context sensitive grammars, not the grammars itself.