Why must sexually reproducing organisms produce sex cells that have half the genetic information (DNA) as they have in all their body cells?

Because offspring with two parents will share half of each parent's DNA.

Explanation:

Sex cells contain half of the genetic information of an organism's regular cells. This is because a sexually-produced organism will be unique; it will share genetic information with both of its parents, rather than be identical to its bearer (like an asexual organism would be). When a sex cell meets another sex cell, their DNA will meet as well and change/adapt to suit the organism. If a sex cell had all the information needed to create an embyro, instead of half, which requires another cell's information to fill the DNA void well, it would just do it.  

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