This question might not be so practical. It's pure curiosity.
Why category in ObjC can't add properties to existing class?
"To add properties to existing class you should use associative reference" kind of answer is not appreciated.
Thanks
EDIT
After reading answers I understand now that it's not true about category can't add properties or more precisely using properties in category. I've tried to declare property in category with custom setter and getter in category implementation. It works fine.
So @jlehr is right this is a duplicate of question Why can't categories have instance variables? and there is a great answer about why