Why Avoid Parry?

[Jpec07]

I don't get it. In 3.x, outside of shields (which are an oddity to themselves), Parry is literally the only pure mitigation stat that we can stack. I understand that Parry isn't "reliable" because it's based on RNG, and that right now, with fights so focused on DPS output, putting any stats into mitigation is a waste.

But in general, don't tanks want to do whatever they can to take less damage? Sure, you can't rely on Parry to save you, but won't it help to smooth out incoming damage when there are a lot of hits coming in? And to that end, isn't Parry then the best stat a tank can get?

So why should tanks avoid Parry, and why is the advice to new players to avoid it?

Edit: Killing a mob faster is only viable as mitigation if the damage prevented is greater than the damage that would have been prevented by instead passively mitigating it. Killing a mob faster to save .3% damage by stacking Crit is not viable as mitigation if a full Parry build would have saved you .5% incoming damage. Is the scaling on Parry really so poor that the DPS gained by using other stats instead makes tank DPS a more viable source of mitigation?