AskUbuntu does already facilitate direct communication between users, through chat. Users can create chat rooms to carry on one-to-one conversations. These rooms are not private, but private communication can be facilitated by using the contact information in a user's profile. If a user doesn't provide contact information in their profile, they probably don't want to be contacted privately by other AskUbuntu users who don't otherwise know them.
Remember, AskUbuntu is a question-and-answer site focused on creating reusable high-quality articles in question-answer form. There are many social elements of the site--after all, communication is fundamentally social. But the purpose of the site is to publish useful information for the community to use; it is not a social networking site. Private messaging between users isn't really part of what AskUbuntu is designed to do, and there are many ways users can already communicate privately if they choose.
Personally, I don't think there would be anything particularly wrong with having private messaging on AskUbuntu, so long as people can opt out of it (so they cannot be messaged), and so long as there is a prominent reminder that it is usually better for the community if people carry on conversations about matters of interest to the community in (publicly readable) chat. But I don't think there is much reason to implement this feature either, and I'd prefer that the development efforts that could go into it would instead be applied to enhancements more tangibly beneficial to our community and mission.