Result of deterioration of vegetation
I think the reason you were marked wrong is because your text book is using the term "climate" loosely.  The deterioration of vegetation will result in desert encroachment ... which in turn can cause a change in local climate.  After all, if you create more desert, you have changed the local climate, right?  However, it takes many years to define a climate period, whereas desert encroachment can happen year to year.  So, eventually the local climate can change... but not if the desert encroachment reverses for some reason.  It's a very fine line, but answer #1 will most certainly occur while #2 may occur afterward if #1 is sustained.