Why can't I connect my private Facebook account with Twitter? It works with the corporate ones I manage, but not my private account.
You can connect your personal Facebook page to your Twitter account - you just can't do this as easily as corporate pages. See this question for details on how to post to both.
As to "why" this cannot be done - I'm afraid no one here is really going to be able to explain the reasoning for this. (Not unless a Facebook employee posts the reasons why).
If you really want to know the reasons why, I would suggest that you contact Facebook directly and ask them for clarification.
To link your facebook and twitter accounts click on this link: http://www.teknoplay.blogspot.com/2011/04/how-to-link-your-facebook-and-twitter.html. It will show you how to update your Facebook status via Twitter.