The Function Module SAP_WAPI_START_WORKFLOW uses RH_TASK_START_CHECK to check, if the calling user is allowed to start the Workflow.
In it RH_TASKS_TO_START is used to read the WF and Task IDs which the user is allowed to call. But it uses a buffer and if you just did some changes to the Workflow Classification, i.e. setting it to General Task,
it can be that this check will continue to fail as it is reading old data from the buffer.
You will receive an error message from Message Class WZ: You are not one of the possible agents of task ‘&1’
I had this problem sometimes when transporting objects to the next system, but until now I could not figure out when it happens and when not.
Luckily the solution is pretty simple, just call T-Code SWU_OBUF and do a buffer refresh/synchronization.
Rob Dielemans has explained the cause very well here.