In general, users don’t have permission to delete the first post in a topic after someone has replied to it. Deleting the first post deletes the entire topic, so valuable replies could be lost too. That’s why they are told to ask a moderator. The moderator could split the replies to a new topic to keep them if needed.
To be able to delete replies or topics without replies, the user must be able to edit their post. The post is not removed immediately; it is first replaced with a “this post was deleted” text. The settings which control how long users are able to edit their posts are post edit time limit and tl2 post edit time limit.