Learning not to worry does not mean you are irresponsible. It means you are sensible!
Worrying is a dangerous occupation. It robs you of the present. One simple way to learn to avoid worrying is to know, to understand, to accept that whatever is due to happen will happen. No matter what. Your worrying about something is not going either make it happen or prevent it from happening.
As you grow and evolve, chances are you will learn this fine art of not worrying. But people around you will not necessarily be at your same level, on the same wavelength. They will keep reminding you that because you are not worrying about something, a grave misfortune is due to follow. Or they will chide you for being irresponsible. Please don’t pander to such views. Worrying cripples you and induces fear. Not worrying is not being irresponsible. In fact, when you stop worrying about something and focus, you will find ways to deal with that something.
Most of us postpone happiness because we are busy worrying. But try this when a worry arises in you the next time. Examine the worry intensely. Ask yourself if your worrying about that specific situation is likely to solve it. Obviously, as you will be quick to realize, it is not. So, do the next best thing – postpone the worry. And concentrate on doing something more productive with your time. Do this over and over again. Day after day. In some time, for sure, you will be happier than you have ever been.