The world of Avatar: The Last Airbender was centered around the journey of a child named Aang. While the young Airbender was revered by the residents of his world as the future Avatar, he still made a lot of bad choices on that path. Those choices cost lives.
It's important to note that Aang was really young, and had the weight of the world on his shoulders. He came through in the end but expectations were high and he wasn't always up to the challenge. Given the situation, it's hard to blame Aang for some of the mistakes he made.
Took His Time On Firebending
Being the Avatar meant learning and mastering all forms of bending. Being that Aang had grown up as an Airbender, he was already quite proficient at that when Katara and Sokka found him. That just left earth, fire, and water. No big deal.
Katara helped guide Aang to being a Waterbender and Toph showed him how to Earthbend. When it came to Firebending, Aang really kind of dragged his butt on his training. There are a lot of reasons why he did this, but none of them change the fact that he extended the overall conflict unnecessarily.
Taking His Friends For Granted
Aang's journey to being the Avatar was long and incredibly dangerous. He had a lot to accomplish in an extremely short period of time. Ultimately, he was successful but he wouldn't have made it if it wasn't for his friends stepping up.
That being said, there were a lot of times that Aang seemed to take the love and support of his friends for granted. They were not obligated to do what they did, though he often acted like that was the case.
Using Katara
At the core of the people who supported Aang was Katara, a Waterbender from the Southern Water Tribe. She and her brother were there when Aang came out of the ice with Appa after a century. They then took it upon themselves to help him on his mission.
While it became obvious that the relationship between Aang and Katara was deepening, he treated her like it was inevitable. Throughout, he assumed that she would help him, and was happy to use her, without really considering what she was giving up.
Avoiding Combat
Taking the high road is important. Sometimes, walking away from the fight is the strongest thing someone could do. Aang knew that, and took a step back from combat situations when he felt it was necessary.
But Aang also seemed to outright avoid conflict more often than not. The Avatar was equal parts diplomat and warrior. There were times that he needed to step up and take the fight to his enemies. Instead, he ran away.
Didn't Take Things Seriously
Being that Aang was destined to be the Avatar, it's easy to forget that he was still a kid. The Avatar was, for all intents and purposes, the leader of the known world. It was a lot of responsibility to be heaped onto a child.
Keeping that in mind, there were a lot of times that Aang just didn't seem to take the situation all that seriously. This would come up early on in the series as Aang often lost focus on his mission and would just end up playing with Appa or Momo.
The Omashu Slide Incident
The great city of Omashu was a special place for Aang before he went in the ice. He and his young friend a powerful Earthbender named Bumi. They would have a lot of fun playing there. After escaping the ice, Aang and the gang returned to Omashu, though things weren't exactly the same.
Before reuniting with a much older King Bumi, Aang showed his new friends the fun of riding the Omashu slide delivery system. The problem was that Aang wasn't really in control of the whole situation and caused a lot of damage.
Lied To The Spirits
Wan Shi Tong was an ancient spirit who collected information and knowledge for his library. The enormous owl had taken his leave of humanity centuries earlier, and generally avoided them at all costs. Aang proved him right.
When Team Avatar made their way to the library, Aang straight up lied to Wan Shi Tong to gain access to the spirit's information. This only validated Wan Shi Tong's belief that humans could not be trusted.
Abandoning The Other Airbenders
A century before the events of Avatar: The Last Airbender, Aang was an Air Nomad. As a powerful Airbender, he spent a lot of time training and enjoying life among his Airbending friends and families.
After he was freed from the ice, Aang returned to his former home and found that Firebenders had wiped out his Air Nomad tribe. Had Aang not run away from being the Avatar, there is a real chance that his tribe would have survived.
Running Away From His Destiny
As a young child, Aang was told that he was destined to be the Avatar. It wasn't welcome news, to say the least. The weight of that responsibility dragged Aang down, eventually causing him to jump on Appa and run away from everything he knew.
But the end result of not having an Avatar to deal with things was the Fire Nation running roughshod over the world, and killing untold numbers of people. Aang made a choice that cost the world dearly.
The Avatar State
As Aang continued to train, he gained more and more control over different types of element bending. And with that increased control, his power continued to grow until he was able to access something called the Avatar State.
The reality of the Avatar State was that it was the ultimate expression of his power, and Aang was barely in control of it. In many ways, Aang was irresponsible with his powers and caused more harm than good when the Avatar State was activated.