The biggest mistake the man made in "To Build a Fire" that led to his death was that he was a newcomer to the Klondike's brutal weather and conditions. He didn't have any life experience that would help him if he needed to survive the extreme cold. He suffered from an ego and felt indestructible. The man didn't realize his own mortality. Another mistake he made was that he went on the trip alone. Even though he had the dog with him, it would have been much safer to travel with a human companion who could, for example, build a fire for him. He also took a journey that was much too long for a "greenhorn" to accomplish. Ultimately, his final mistake was that he got wet falling in the creek. He was unable to read the signs of thin ice due to his inexperience. After getting wet, the man panicked. He knew that he had to build a fire to survive, and after a few attempts, struck and lit all the matches at once causing the sulfur smell to make him drop the matches in the snow. If he had remained calm, he might have been able to start a fire that would have saved his life.
Overall, the man's inexperience and "cocky" ego killed him because, unlike the dog, he didn't have the animal instincts to survive.