I want to be able to delete previous progress.
Just so we're clear on what you're requesting - when you say "delete previous progress" are you thinking about completely eradicating previous progress such that it does not even show up in the reference browsing? If so, I tend to agree. I have added this to our "serious consideration" list for future improvements.
As an aside, you can remove passages from your My Verses list by going into My Verses and hitting Edit on the top right. Then you can tap the red circle to take passages off your list.
You won't be notified about changes to this idea.