Firstly and most obviously, in a sensitive environment such as the White House, controlling the flow of information to the outside world is extremely important. Secondly, Twitter is not immune to malware, viruses, and scams. Then there is the Presidential Records Act, which requires all White House communications to be saved. Abiding by these rules would prove difficult on an external service such as Twitter.
O'Brien also explains why switching to free Firefox would actually be rather expensive.