Hello Dor Zigdon Lax ,

You can delete your posts as follows 

Replies will also however be deleted if you started the thread.

Hello Steven,

Thank you for your comment. The Delete menu item doesn't display for me as shown in the following screenshot. I can only delete my comments in a thread, but not a thread I started (or its original post).

Hi Dor Zigdon Lax, 

You can only delete your own post when there are no replies to it by others. So this post triggered an answer from Steve and because of that you cannot delete this post anymore.
It works this way to prevent the deletion of other persons contributions. 

To make sure that there is nothing wrong with your Community account setup, I used my admin rights and tested it using your account. See below.
I created a post, and used the delete option to delete it again. It all works as designed. 

I hope this helps,
  Regards,
     John