若\emph{x}，\emph{y}，\emph{z}均为正整数，则下列不等式中不一定成立的是（~~~~~~~）
选项为:A:$\left(x+y+z\right)\ln \frac{x+y+z}{3}\geq x\ln x+y\ln y+z\ln z$  B:$\left(xyz\right)^{\frac{x+y+z}{3}}\leq x^{x}y^{y}z^{z}$  C:$x^{2}+\frac{1}{x^{2}}\geq x+\frac{1}{x}$  D:$\textbar{} x-y\textbar{} \leq \textbar{} x-z\textbar{} +\textbar{} y-z\textbar$  请回答其中一个选项.