Why is it that some people will blame others for their misfortunes yet excuse themselves of responsibility when they fail? Do you do that too? What can be done to avoid the fundamental attribution error and the self-serving bias?

That is a very good question and it has a lot to do with ego and pride.
People in general look to blame others for their misfortunes, like when they are running late for the train miss it then blame the train guard or driver, they can not blame themselves for  being late it is always someone else's fault. The problem with blaming others for our own misfortunes is that we never learn from them and are therefore "trapped" in repeating the mistake over and over again. It is very beneficial to accept our failures and learn from them so that we can improve and move forward.
In Schools we are taught not to make mistakes and we are punished and ridiculed for our errors therefore we seek to blame others for our mistakes.