It takes maturity for someone to be responsible. You can be hold enough to be accountable for yourself and others, but still not responsible.
Being responsible means that you take your duties seriously. The older you get, the more responsibilities you have. You have work to do, chores to finish, siblings or children to take care of, homes to clean, foods to prepare, bills to pay, relationships to uphold, and other duties that need your attention.
Some people are unable to take on responsibilities like they are expected to. Instead of becoming more accountable, they spent their adult life dodging responsibilities.
Adulting comes with more responsibility. You cannot expect your parents to continue taking care of you, feeding and clothing you, doing everything for you, paying all the bills, and taking care of your children too.
As you become an adult in your own right, you should look out for the open opportunities around you. Gain skills and find a job or start a business to help you take care of yourself and stand up on your own.
Your parents can help if they can, but you should get to a point where you can be responsible on your own too. Sometimes life can get tough out there. You may become broke and lose your job or apartment.
When that happens, go back to the drawing board and start all over. If it's necessary, you can always go back home and restart from there. See where things went wrong and find a way out.
And when you find that you did something that hurt someone else or you made a mistake, remember that taking responsibility is always the best thing to do. It may not be the easiest, but always own up and apologize. Here are responsibility quotes to give you more insight.