That's not my X, its Y is too Z
Python 3, 149 bytes



lambda a,*l:shuffle(a)or["That's "+s%(a[0],*map(choice,l))for s in["not my %s, its %s is too %s."]*5+["my %s! Its %s is so %s."]]
from random import*


Try it online!

-9 bytes thanks to movatica