Arrogant, rude, and insolent, Alex Karev had been established as a polarizing character on the ABC medical drama Grey's Anatomy, an outlier who didn't care how many people he ended up hurting. Whether taking pleasure in being a jerk to the adorable George O'Malley or humiliating Izzie for having had a modeling career, Alex was a deeply insecure person for several seasons until he mellowed and evolved into a great surgeon.
As his character started on a developmental arc, he gradually started showing traits that were admirable, to say the least. Alex was a great friend, a survivor, and cared genuinely for his patients. He also cared for one woman, Izzie, his whole life, which was totally adorable.
Worst: Arrogant & Offensive
Alex was well-known for his arrogance towards almost anyone and everyone, irrespective of whether or not they were friendly such as Izzie Stevens. In fact, when he first joined the show, his character was introduced as some kind of foil to the gentle George to whom he was nothing but a jerk. He refused to be respectful in his ways and ended up offending almost everyone that worked with him.
Best: Cares Deeply
Alex Karev went through a tremendous evolutionary arc over the years, and, in time, he was shown to care deeply for the people he was attached to, whether it was someone he loved or his patients. He cared deeply for Izzie and Ava, although his feelings for the latter were misplaced. But, he also cared for his little patients to the extent that he flew all the way back to Seattle to save a baby who needed him, consciously putting his career in jeopardy as he was late for his attending exam.
Worst: Immature & Selfish
When Alex started out, he was self-centered and thought of no one but himself. He was the last person one would go to for help, and he rubbed everyone up the wrong way with his selfish ways.
Even when Izzie was terminally ill and had just had her surgery, Alex seemed to be more concerned about his own misfortunes rather than the terrible ordeal Izzie was going through. True, his outburst, telling Izzie that she was going to be a burden on him, came at a moment of despair, but it did reveal him to be grossly immature.
Best: A Good Friend
Alex, in time, became a wonderful friend and a pillar of support—at least to Meredith. The latter even considered him her 'person' after Cristina had left, and especially after Derek passed away when she needed someone to turn to. Alex, in his own way, tried to be there for his friends, and, given how he knew next to nothing of friendship or support for a very long time, this was a commendable effort.
Worst: Condescending
Alex was condescending, to say the least, whether it was toward the nurses or men who were softer and kinder than himself such as George. His condescension extended to the Pediatrics and the Obstetrics departments, which were considered less glamorous or heroic than cardiothoracic, neurosurgery, or even plastics, the last of which he wanted to specialize in because it paid the most.
Best: Has A Fighting Spirit
Alex was revealed to have had a difficult childhood and adolescence, during which he had to look after his siblings and his mother, who suffered from schizophrenia.
His dad had been addicted to drugs and abused his mother before abandoning his family altogether. Alex had spent much of his time around foster homes as a teenage boy. The fact that he managed to survive these times and become a brilliant surgeon in his own right showed that he wasn't one to give up easily and had a fighting spirit.
Worst: An Inclination For Physical Violence
Unfortunately, for every good trait that Alex had, he had several questionable ones, as well. His tendency to become violent was one such trait that landed him in trouble more than once.
For instance, Alex had beaten up his dad as a young man when he became a wrestler to save his mom from being physically abused. This was a gesture of love for his mom on his part, but this inclination of his stayed with him. He punched his dad years later when they met at the bar, and, of course, he beat DeLuca into a pulp on the assumption that he was attacking Jo. Although he took to violence only when he wanted to protect someone, these habits definitely seemed to be unhealthy.
Best: Believed In One True Love
Alex Karev believed in one true love, and, for him, his one true great love—or soul mate, as Meredith put it—was Izzie Stevens. Alex implied to the latter that Izzie was his true love while reminding her that Derek had been hers.
For someone who had gained some notoriety for sleeping around, to ultimately settle for one woman had seemed impossible at first. However, he did eventually when he left Jo to be with Izzie and her twins in order to give his kids the childhood he had never had.
Worst: Impulsive & Erratic
Alex's decision to be with Izzie was hailed by some fans as the only resolution that made sense for the character's abrupt departure from the show.
However, it can't be denied that it was an impulsive and erratic decision on his part to simply abandon Jo whom he claimed to love and had married for an old flame. He didn't even speak to her face to face and lied, saying that he was with his mother, whereas, in reality, he was already at Izzie's. Saying goodbye to Jo and his friends and mentors in a Dear John letter was too season-one-Alex, and his sudden whim took the character back a few years.
Best: Inherently Good
Alex Karev was inherently good, and it transpired by and by that a lot of his arrogance was the result of a deliberate defense mechanism. He was usually trying to prevent himself from getting hurt, which made him behave rudely to others to keep them at arm's length.
The way he took the reigns of the Peds department when Arizona was going through a tremendous ordeal following season eight's plane crash, postponing a dream fellowship position at Johns Hopkins, showed that underneath his arrogant exterior he was a good man. He also gave himself up for having beaten DeLuca, which was decent of him.