Understand why passwords cannot be changed in Azure AD sometimes

Q. I'm trying to change my Azure AD password using the portal but it says I cannot change my password there. Why?

A. If you have accounts that have been populated in Azure AD from AD then as part of that replication it is possible to replicate the password hash and have passwords that are changed in Azure AD be written back to AD HOWEVER this writeback requires the user to be licensed for Azure AD Premium. If the user does not have an Azure AD Premium license and their account is sourced from AD then in order to protect against password fragmentation the user will receive an error that their password cannot be changed.