Why are siblings unidentical? (Which chromosome of the pair do gametes have?)
The gamete doesn't "choose" one or the other.  Both are made and you get two gametes, one for each. 

Also it's unlikely to be an "exact copy" due to recombination and random or independent assortment.  There are also smaller influences on genetic variation, and epigenetics, but at this level of question I think you should focus on those two.

Was this homework?  If so it should be tagged.