Why do Mormons have family dress them for burial?

Having family members dress the deceased for burial is a tradition within the Church of Jesus Christ of Latter-day Saints (the 'Mormon' church). It isn't a requirement. If the family is unable or does not wish to dress the deceased, it is often done by someone from the congregation or by the funeral home/mortuary.

The Church Handbook of Instruction says that male leaders in the congregation may be asked to dress deceased males and female leaders in the congregation may be asked to dress deceased females. (see sections 18.6.2; 7.10.2; and 9.10.3)

These guidelines of having family or congregation leaders dress the dead really only apply when the deceased has been endowed in the temple, as it is expected that they will be buried wearing the ceremonial temple clothing, or that it will be folded and placed in the casket. If a deceased Mormon was not endowed in the temple, they will not be buried with the ceremonial clothing and can be dressed by anyone - usually the mortuary.