I can see why it might seem confusing, with one set of values seemingly contradicting the other and yes there are those that choose to live their lives totally under anothers control as truly subservient, without limits or opinions however I'd say that's the minority of cases. For most d/s couples you can think of it in terms of being the submissive that chooses to submit, the submissive that chooses the boundaries, limits and rules, the submissive who keeps the ultimate veto (her safeword) and therefore the dominant is one who merely facilitates the submissives desire to be controlled whilst giving her the freedom to be herself and talk, laugh, chat, work, dance, sing, enjoy our hobbies, etc, etc.

Sure you will likely be punished and have to do things you may not enjoy so much as a submissive but look deeper into that and you'll find it's only happening because you choose to submit, you chose to allow it on your limits and at the end of the day you can just say no and stop. Everything should be done through careful discussion, open and honest talking and making sure that both dom and sub are happy and getting everything they both need - you can't get more equal than that.

You still have equal rights as a submissive -- bdsm doesn't replace that it just naturally sits alongside our every day values and beliefs as this wonderful, sensual and kinky world of delights