For some reason Cass’s wings were really bothering him. He couldn’t fix the issue himself so he had to go to someone. Dean and Sam were on a hunt so his only option was you or Jack. Which he felt that you would actually be able to figure out what was up more than Jack

It takes a deep sense of trust for an angel to show their actual wings and not just the shadow version. It took an even bigger deal of trust to let someone touch them mostly because angels’ wings were…. very sensitive