You didnt explain why bitcoin is valuable! I explained to you why people want gold and dollar. You said bitcoin is rare and thus valuable. Well that is a description of its quantity not bitcoins value. If I say a deadly insect is rare do you think its valuable? Of course not.
First of all, you're confusing me with someone else, because I never said that bitcoin is rare and thus would be valuable. Secondly, people would want dollar and gold because dollars and gold have importance to them as means for the achievement of their desired ends. That's what subjective value actually means...