The reason Peter uses his powers responsibly is because he does not do anything to stop the burglar who ends up killing his uncle. This relates to people learning from their past mistakes and moving forward. This really relates to the people of the time period when Spider-Man came out. There was a lot of racism and sexism going on at the time. Consequently, people seeing Spider-Man move forward from something so drastic, helped them realize that they could move on from their past mistakes as well.