By default anonymous users are not allowed to manage users. When you are not logged in, you are an anonymous user. You can grant needed rights for a given role (Anonymous) from Settings >> Permissions section of Sitefinity's backend. Or grant the rights to users who would then have to be logged in to change their password.
Or you can get around the security check for just this action in code:
the Telerik team
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Public Issue Tracking
system and vote to affect the priority of the items