You can delete your posts manually; Bitcointalk doesn't have a "delete user" feature.
Or did you mean he can edit his post? Because no user can also delete post. But a post can be edited to del and also be reported to moderators for a moderator to delete it. But the post can not be deleted/removed by the user. Or probably it is a typo and you meant can't delete.
I think you can delete your personal posts on threads after 24 hours but cannot delete a thread you create yourself and that’s what I thought he meant.
I am not referring to other posts but topics. You can delete you lost immediately after you post it, but on some board like service board which I noticed, you will have to wait for 24 hours before you can delete your post there. But if it is a topic, you can not delete it.