Your supervisor is there to help you reach this stage of self-reliance. This does not of course mean that you should try and train yourself never to ask for help, and to do everything by yourself. On the contrary, you should ask for help, but you should be as demanding of yourself as you are of your supervisor. It is not up to them to provide you with research topic, methodology, re-writing skills, annotated bibliographies, secretarial assistance in the form of proof-reading, etc. This is your responsibility and it is what you are awarded your PhD for learning to do.
The supervisor’s role is to read your work, to engage with it critically, to provide you with helpful responses and readings, to suggest ways of developing your analyses, to point you in the direction of interesting new sources and generally to make sure that you are progressing through the stages of a research degree as you should be, ie. getting work in on time, maintaining a high standard, and that the work that you eventually submit for examination as a thesis meets the requirements. Yet, above and beyond these crucial intellectual and administrative roles, they aim to support you in your work, to give you the encouragement you need, to deal with problems of any sort as they arise, and to induct you, through example and encouragement, into the academic life. They will be mentor and sometimes friend, and a good working relationship with an engaged supervisor can be one of the high points of your PhD. It is often an immensely stimulating experience, emotionally as well as intellectually, for both sides. Your supervisor will probably continue to be an important person to you for many years to come, not least in the sense that in many cases they provide references for jobs.
All of which reinforces the point that it is important to get the supervision process, not to mention the supervisor-supervisee relationship, right.