Where avoidance was
It's weird that, even in WoW's past, when avoidance stats were as plentiful as the buffalo once were, they were never particularly that great. They were awesome on Brutallus, for example -- and that's my only example of a fight avoidance was amazing for. Which is sad to say.
Between gearing having triple secondary stats on gear and the defense stat (which was mandatory to stack) also imparting avoidance, we tended to have a ton of dodge and parry. So much so that diminishing returns were added in Wrath to keep numbers from inflating too high, and then in addition Chill of the Throne had to be implemented in the final tier because unintended gear inflation had allowed it to get nearly as bad.
And yet, regardless of the quantity of avoidance we have, there was always a noticeable lacking in quality, as stamina and armor were better stats to focus on. All avoidance stats had going for them, honestly, was ubiquity.
Regardless, Blizzard didn't care for how out of control avoidance numbers were at the end of Wrath, so they engaged in a significant reform of tank gearing. All characters received huge health boosts and avoidance stats were severely curtailed between even heavier diminishing returns, the axing of the defense stat, and the harvest performed on the talent trees.
Fast forward to today in Mists and the situation has only gotten worse from avoidance's point of view. Active mitigation has completely eclipsed avoidance (the very definition of 'passive') and become the be-all-end-all of tanking. Through their attacks, tanks are now personally contributing to their mitigation and not just depending on the favor of some invisible random number generator to flip in their favor.
Where does avoidance break down?
The actual problems with dodge and parry are two-fold: one is an objective, mechanics argument and the other is more subjective and concerned with look-and-feel.
For starters, the tanking game (as I alluded to) is very different in this expansion compared to previous ones. The introduction of active mitigation and the explosion in the numbers of cooldowns at our disposal has turned what used to be a mostly-passive affair into a very different style of gameplay. This has also lead to a huge shift in perception as tanks approach their stats very differently.
Hit and expertise make your attacks connect so you can accumulate the resources need to use your active mitigation abilities. Mastery makes your active mitigation more effective and potent. Haste and crit (for some classes) make you accumulate those resources more quickly, so you can use active mitigation more often. These are 'deterministic' stats, which means they help you choose when you want them to boost your survivability. You can line them up with when you need them the most.
On the opposite side of the coin are dodge and parry, which are 'stochastic' (a fancy way of saying they are random). They may help you, they may not.
Considering the tanking paradigm these days has shifted towards favoring deterministic spike reduction, the gear we gravitate to is going to match that. When you have mountains of sims, formulae, and theorycrafting pointing to the superiority of smoothing out your damage, why would anybody want to choose gearing that goes against that and emphasizes an outdated form of tanking?
Furthermore (because this is a game we are playing after all) it's important to approach the issue from the perspective of actual gameplay and this alien concept called 'fun' that we tend to overlook sometimes. Whenever haste is in peril, the first kneejerk reaction of paladins is often "don't nerf haste, it's so much fun!" Have you ever heard a similar argument with regards to avoidance?
Dodge and parry are nearly invisible in day-to-day tanking, if only because they are so passive and out of sight. When you're actively grappling with a boss, what is more likely to grab your attention: your character quickly dipping to the left for a brief moment (though perhaps that animation was lost in a sea of spell effects and the dance between tank and target), or a big sexy number because one of your active mitigation consumers just crit with a large stack of Vengeance?
Some tanks have a mechanic, like Revenge, that allows them to use a special ability when they avoid an attack. This can absolutely be fun, though in the case of Grand Crusader (for example) being able to use Avenger's Shield outside of GC somewhat takes away from any specialness that seeing the proc might otherwise impart. This is definitely an avenue where they can improve the look-and-feel of avoidance, though ultimately it will still suffer from that randomness problem.
As an aside, it's interesting to consider how many tanks approach stamina (and armor), which is just as passive as avoidance. Yet we nonetheless get perverse joy out of how high we can get our hitpoints to max out at, we look forward to higher ilevels to add on even more stamina, and we chuckle with delight as upgrades make various boss attacks weaker and weaker against us week after week. I guess the difference is that you can have a representation of your stamina on your screen at all times (your health bar) and avoidance only makes brief appearances from time to time. (There's that randomness factor again.)
Something needs to change
Before I go any further, let me step back for a moment and clarify that I do not think that dodging and parrying needs to be removed from the game. What I do think needs to be reworked though is the presence of dodge and parry stats on tank gearing.
For the duration of Mists, there's been this tug-of-war game between Blizzard and tanks, where the former is struggling to bring tanks over to their point of view that dodge and parry gear should be just as worthwhile to collect and equip as any other gear. On the other side of the rope are tanks who are utterly convinced that every single point of dodge and parry rating that they accumulate on gear is wasted itemization if the alternative can be something far more interesting and pertinent to our tanking playstyle.
Leather tanks already live in the Promised Land. They are not saddled with any dodge on their gear, tanking leather having been purged from the game expansions ago -- a fact that many plate tanks may be unaware of. To be fair, that is mostly due to there having only been one leather tank spec -- and this privilege continued when the current expansion launched with a second.
There have been some encouraging steps in the right direction in the 5.4 PTR. The strength tanking legendary cloak was recently changed from dodge/parry/mastery to expertise/parry/mastery, which is wonderful. Likewise, the stats on the new protection paladin tier set are also good news. There are no dodge+parry pieces and (even better) a few have haste on them! This is a milestone for plate tank gearing: official, itemized recognition that haste can be a tanking stat.
Now, granted, I do recognize it would be difficult to go whole-hog and mash three tank specs and five DPS specs into the same pool of gear without creating new (social) problems. Parry and dodge do have the fortunate effect of delineating which gear a tank can look at and go "this is for me." I don't know any easy solution to get around the strife that would likely emerge.
What I do know, though, is that the system is broken and something needs to give. Avoidance, what are considered to be two of the main tanking stats, are junk. There needs to be a change in the equation to either make avoidance much better for active tanking -- and that means adding some sort of hook that harness its random nature into an active bonus -- or just finish the job and remove it from plate gear outright.
At the very least, Blizz, no more itemizing gear with both dodge and parry. Please.