Yes, it's a permission issue, The site Owner can only deactivate and delete the
Site Template that already not used.
At the other side, the
Site Collection Administrator is responsible for the entire site collection and can deactivate and delete a
Site Template that already used or not.
So you should be a
Site Collection Administrator to be able to deactivate and delete
Site Template that already used.
Note: Once the site is saved as a template it saved in
Solution Gallery below
Web Designer Galleries in the Site Collection,
Solution Gallery is not available in sub site
Site Owners are responsible for one part of a Site Collection only, and cannot change anything on Site Collection level. They have full control on one or more subsites, and can grant permissions to users, create lists and subsite ... etc
Site Collection Administrator: is responsible for the entire site collection, has to access to Site Collection wide features in several places including Site Settings, Solutions Gallary ... etc.
Read more about The difference between Site Owners and Site Collection Administrator