Classes: Worgen Paladins 
The question on why worgen can or cannot be certain classes is one of controversy. But it almost always comes down to defining the class, defining the race, and asking if the two make sense together. Firstly, a worgen is not a human. Worgen are beset by animal instincts, the need to hunt, and unbridled rage. Secondly, paladins are not priests. While they do serve the Light, they do so in the thick of battle, as holy knights and steadfast guardians, and are specially trained in patience and justice.
What is a worgen?
Worgen are humans[1] or kaldorei[1] who have contracted the worgen curse, becoming one themselves; a creature balanced between man and beast. Some are able to shapeshift, resuming their prior form for a time, but all worgen - even especially Genn Greymane[6] - feel the call of the wild and hunt prey on all fours. A seething rage courses through their veins by from the same source as their instincts and lupine features; the wild god Goldrinn. It is the presence of Elune in the curse - the goddess of balance and of change - that keeps the lupine essence of the white wolf balanced with that of the man[3]. Even then, “balance” is a constant struggle[5], with rage, instinct, and humanity. Those that experience great turmoil may lose themselves to despair[9] or panic[8], falling into the Mindless State, a mental state of bestial fight-or-flight.
Cited Sources
[1] Curse of the Worgen Issue 1
[2] Curse of the Worgen Issue 2
[3] Curse of the Worgen Issue 3
[4] Curse of the Worgen Issue 4
[5] Curse of the Worgen Issue 5
[6] Wolfheart
[7] Lord of his Pack
[8] Gilneas questline
[9] Duskwood questline
What is a Paladin?
A paladin is a holy knight embodying discipline, virtue, justice, as well as compassion, patience, and goodwill. Where a worgen is a juggernaught of Goldrinn’s rage, a paladin must be a disciplined conduit of justice. Where worgen instincts demand survival at all costs, a paladin is sworn to bravery. When enraged, a worgen will use claw and fang to eliminate their prey, while a paladin is charged with controlling their emotions and defending the weak. While worgen are quick to anger and emotional, paladins must be patient, understanding, and just.
This comparison is drawn well in the novel Before the Storm, as we see the worgen Genn Greymane and the paladin Turalyon. Both serve as advisors to King Anduin Wrynn in the novel. Both are faced with various situations while they serve their king, from inspecting bodies slain by Dark Ranger arrows, to reacting to the concept of Forsaken welcomed into the Alliance, to meeting a very special forsaken and old friend. In each situation, the two characters react differently. One as a worgen, and one as a paladin. Genn reacts with rage, quick to act and seeking violence. Turalyon on the other hand, while he does grow angry, he maintains patience and composure, and even comes to see the forsaken - his former teacher - as a friend once again.
Tome of Divinity
“In all things, paladins must reflect the Light, which supplements our strength. To strive to be divine for one of our kind does not mean we strive for godhood–we strive to be good in all actions. Although called upon to smite evil in these harsh times, you must always remember that it’s aiding others that will truly set you apart from the other citizens. Compassion, patience, bravery–these things mean as much to a paladin as strength in battle.” – Tome of Divinity
Before the Storm
Turalyon had no sword and wore no armor. Yet he still loomed large and powerful in the cathedral as he straightened to his full height. If Genn had been racked by anguished fury, Turalyon, one of the first paladins of the Silver Hand, was brimming with righteous rage.
Golden, Christie. Before the Storm (World of Warcraft) (p. 211). Random House Publishing Group. Kindle Edition.
Worgen Paladin?
Impossible vs Improbable
When it comes to races and classes, I have long used “impossible vs improbable”. Meaning, while it may or may not be impossible for a Forsaken to be a druid, it is definitely improbable. Draenei warlocks, human shamans, goblin druids, tauren rogues, all very unlikely due to the nature and culture behind the race and the definition of the class. There may, however, be very rare particular cases, where such reach the cusp of possibility, such as the human shamans in Stranglethorn, or the goblin naturalist in the Hillsbrad Foothills.
Flaw vs Cause
Another point, however, is that “flaw does not justify cause”. Some will argue that because worgen are full of rage, they would benefit from becoming monks. Or that because worgen are undisciplined, they would benefit from becoming paladins. However, this is akin to claiming that a blind man should become an artist, or a cripple become a ballerina. True, crafts or physical therapy are hobbies worth pursuing, but it would be significantly more difficult to become an artist of renown.
Yes, a worgen could learn meditation, and could worship the august celestials, and maybe it could help a worgen find balance. But that rage will never leave, and a worgen soul will never be at peace. As Belysra Starbreeze says in Curse of the Worgen issue 5, “Your feral side will never fully be at rest”. Likewise, there is nothing stopping a worgen from following the Light, and it is in fact still one of the dominant religions among Gilnean worgen. To become a champion of the Light, however, would require patience and discipline that worgen are incapable of, thanks to the nature of worgen.
Conclusion
That said, there are exceptions to the rule. Calia and Lothraxion are one-of-a-kind exceptions, where something has defied their nature by making them into entirely new beings. There may very well be a worgen paladin in the future, but - like a demon becoming a paladin - it would require divine intervention and a change to their nature, or otherwise would be exceedingly rare.
Thankyou for the question Mevaar! The question of worgen paladins is one as old as the playable race itself, and was a topic of great debate on the old forums, all of which have since been wiped. So bacons to you for giving me the chance to revisit that topic here on the new forums. 