Answer
One problem with dividing-before-duplicating would be fact that the daughter cells would end up with different sets of chromosomes since the homologs received from each parent are non-identical. This would lead to an organism which was a weird mosaic of genetically non-identical cells, which might lead them to cooperate poorly.
Work Step by Step
The key here is to recall that mom's chromosome #1 and dad's are non-identical, so dividing before replication would leave some cells with mom's chromosome and some with dad's. The entire genome would need to be split before replication, meaning each daughter cell would only have half the pieces of its genome that it may need to function properly.
