After a long night of arguing, here is where we are: She wants me to understand and acknowledge how I have hurt her, and she wants to feel comfortable that I won't hurt her again before the relationship can continue.
How have I hurt her? By making my continued participation in the marriage conditional upon having a physical relationship with her.
I refuse to apologize for this. This is who I am. If placing this condition on our marriage has hurt her, then so be it. It is a perfectly reasonable condition in a general sense, and it is, to me, a basic, important part of a loving marriage. If this condition has hurt her, the hurt has come from some place inside of her, not from me.
