Why questions are often difficult to answer but you seem to have a very
reasonable answer to explain your observation. To really confirm that the
nongreen parts of your variegated leaves do not photosynthesize as much as the
green parts, you would need to do one of the following:
1. Starch test the leaves to show that there is little or no starch in nongreen
areas and lots of starch in green areas. This may not work on all leaves
because some plants do not accumulate starch in their leaves but export
photosynthates as sucrose.
2. Extract chlorophyll from green and nongreen areas to show the nongreen areas
have little or no chlorophyll while green areas have lots of chlorophyll. Just
because a leaf is nongreen does not mean that there is not chlorophyll there.
In some nongreen leaves, other pigments such as carotenoids and anthocyanins,
simply mask the green chlorophyll.
3. Measure photosynthesis in leaf disks cut from green and nongreen areas of
the leaf to show that photosynthesis occurs in green but not nongreen parts.