Arthas is a complex character, as his decisions were not led by a straightforward "Le ebil" path, but him losing his way for the sake of the greater good, road to hell paved by good intentions and all that shit. Paladins in WoW utilize the light, which requires you to be righteous (but not exactly good) all the time, and Arthas at the time of the culling was a paladin in training.
He had history of losing those he loved before due to his own mistakes, such as how he had lost his horse, Invincible, due to a terrible snowstorm that had hit lordaeron. He made Invincible try jump a ditch to reach the kingdom much faster, and it resulted in Invincible breaking a leg. When this happened, Arthas wasn't a paladin yet, so he didn't have healing light magic. All he could do at that point was mercifully put his horse down, and live with the guilt. This is one of the many instances where arthas has carried a lot of heavy shit on his back leading to the culling. Now, we go to his story in wc3. Essentially, his story is the question "Can good people become bad".
Imagine this, you see a bunch of orcs taking people prisoners and sacrificing them, failing to save them and thus your only option is to slay the orcs. Then, out of fucking nowhere, plagued granaries start showing around and the dead rises up. Not only you find cultists razing towns and using the dead as their own armies, but you then see a necromancer taunting you about how your future is set and everything you do is meaningless. After you slay him, you try to go to a neighboring town to help before the undead raze it... until you see that the plagued grain had already been distributed in that town, thus you see everyone turn into zombies.
No matter what you do, the undead keep rising and everything keeps getting fucking worse. There seems to be no solution, nobody can come up with a good idea, not even the most powerful wizards at the city of wizards. So, you rush to another town to try and stop the dead and their leader before they attack another city (Stratholme). And when you reach it? You see everyone's already infected, and it's only a matter of time they turn.
Your only logical solution is... to purge them, to spare them from a horrible fate. And when you suggest this? Your love interest, your mentor and half your army deserts you. You're all alone, to carry what you believe is right. And, once you do and follow the undead to a cold north, you start doubting yourself. Start asking yourself if what you did was right. And because you did that... your power starts waning, as the light requires you to be righteous. Only to lose your sanity the more you stay in the cold north, only thinking about revenge, being blinded by the one who did this to you; The leader of the undead Mal'ganis. Who keeps taunting you. Who lured you to follow him to the cold north. All you can think now is to kill him.
You find an old friend, who you naturally help given he's also fighting the undead. But not too shortly after, your mentor convinces your father the king to recall all your troops. In a bit of insanity, you burn the boats down, and at the recommendation of your friend, look for a sword to take sweet revenge... even if it costs you everything.
TLDR; Arthas is a very flawed character, and whereas he was right or not is heavily up to interpretation. But calling him an "irredeemable piece of shit" is the most fucking retarded take ever because it goes against everything the entirety of Warcraft 3: Reign of Chaos was setting up. Including later campaigns such as orcs redeeming themselves after years of being putrid.
My hopes are on you Bela. You can find all of what Opal posted here to cross check what the man in the ghostbuster car will say. Just don't lose your way and get lost like that one idiot did a few pages back.
