There are two main reasons. First, I'm leery about the bio-hazard issues of dumping used kleenex in a home compost system - home systems usually have slow and incomplete decomposition and I'd worry about coming across contaminated material in the garden soil. Second, many kleenex manufacturers put additional chemicals in their product, from perfumes to moisturizers, and a home system doesn't usually have the volume to dilute such things to inconsequential levels.

YMMV, of course.