Hi Andrii - Welcome to the Atlassian Community!
Permissions to modify data are based on the Permission Scheme associated with the Space. Just being a Jira Admin or being the creator of the stories does not give you automatic permissions to delete stories/work items. So be sure you have the permission to delete work items in the Permission Scheme. It is a good idea to use the Permission Helper while on the Permission Scheme to guide you.
Now, having said all of that, it is not a good practice to delete work items in Jira. I suggest you modify the workflow for the project to include a Status for Canceled or Aborted or Abandoned or something like that. Then move the undesired or not needed work items to that status.
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