Look if you really eager to know the scientific reason for short height of girls is mostly hereditary such as from your mother. you must checkout your mother's height before thinking. Another reason could be lack of nutritious diet and hormones secretion. 
hope it may be useful to you. thank you 
But y it doesn't happen in boys..?
no it is not like that .. genetic traits are same as parents characteristics it wont be changed. ... but as u said it doesnt happen in boy , i would like to say in girls body grows faster at the age of 14-16 almost 97% of ur height and at 17yrs it stop but in boys height keeps growing till 18 yrs and it has scientific reason .
Ok ty very much
oh it was my pleasure .. always welcome
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   It is true that in most of the species especially mammals, the males are stronger, taller and bigger in size than females.  It had been so since ages.  This is true with in a society.

   Women have oestrogen hormones while men have testosteron hormones which make them different in terms of reproductive function.  Perhaps they also cause indirectly certain traits.  The endocrine system regulates the body functions relating to metabolism, respiration , reproduction and others.  Usually the growth (in height) stops in girls three years earlier than in boys.  That could be another reason.

    It is possible that during the time of apes the women preferred men who are bigger.  It is possible that male species fought for females and only stronger survived.  Due to the (sexual or otherwise) preferences of women, the taller, stronger and bigger male species survived.  Such males caused more reproductions.  It is possible that evolution took place in the direction of preference selection of women. 

   Since that time, due to the hereditary nature (ref: genetics), men have been always bigger than their contemporary women in any one particular society.
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Ty very much