You can only delete a group from your phone if you're a group admin and remove each participant. After removing all participants, you'll need to exit the group in order to see the delete group option.

Remove a participant

1. Open the WhatsApp group chat, then tap or click the group subject.
2. Tap or click the participant you wish to remove. Then:
   • On Android: Tap Remove {participant} > OK.
   • On iPhone: Tap Remove from Group > Remove.
   • On Web/Desktop: Click Menu by the participant's name > Remove > REMOVE.

Related resources:

How to exit and delete groups: Android | iPhone | WhatsApp Web and Desktop