To me, "自己的事情自己做" means that we should always TRY to do the things that we're responsible for (washing cloths would not be a responsibility of a three-year-old's). However, this does not mean that we're always able to produce to the best, or intended, results, in which case, we would need some help. We should always be ready to lend that help when others are in need of it. This is either to improve the way we do those things or to achieve a better result through teamwork and sharing of knowledge. This is "积极热心帮助别人".:blowzy: