You might want to just have a time limit for them to change their mind or someone might post a lot then delete all their posts leaving a lot of holes in the conversations later.
It can be two edged sword. As if you allow them to delete their post malicious people can cause havoc and then delete their posts to erradicate all evidence.
There are some software, that allows seme deletion, as it member won't see the posts, but admin can still see them. This means that you can delete them for good if you want while still giving the users some of the control.
I like having the option, as a member, specially when I accidentally post twice the same post, or if I changed my mind on something.