Example 31 (2004 College Entrance Examination Hunan Paper) Given $a>0, b>0$, which of the following inequalities does not always hold? ( ).
A. $(a+b)\left(\frac{1}{a}+\frac{1}{b}\right) \geqslant 4$
B. $a^{3}+b^{3} \geqslant 2 a b^{2}$
C. $a^{2}+b^{2}+2 \geqslant 2 a+2 b$
D. $\sqrt{|a-b|} \geqslant \sqrt{a}-\sqrt{b}$
Solution: Choose B. Reason: Assign values to $a$ and $b$, let $a=2, b=3$, then $\mathrm{A}, \mathrm{C}, \mathrm{D}$ all hold true, with $a^{3}+b^{3}=35, 2ab^{2}=36$. At this point, $a^{3}+b^{3}<2ab^{2}$, therefore B does not always hold.