I did something genuinely terrible.
I think I can help, can you tell me what you did?
I told the police that I could be the person who robbed a bank yesterday. I feel terrible about it too.
It is great that you are coming clean, you are giving the officers an easier time to figure out what happened. It's not forgivable that you robbed a place, but at least you are showing remorse to not do it again.
I had other reasons, they should understand.
For whatever reason, it will be good to make it right. I am proud of you for being honest even if there are other reasons you want to keep to yourself.