Insurance companies have a managed care component that requires more information about you and can determine how often and/or how much therapy you can receive. A mental health diagnosis is always required when an insurance company is billed for services.
Some insurances require written information about your treatment, sent either electronically, faxed or mailed, with a determined number of sessions specified; which does not allow you the freedom and flexibility you would get when your therapy is paid for out-of-pocket. These restrictions also apply when you pay out-of-pocket and then turn the claim into your insurance.
If privacy and confidentiality are of significant importance to you because of your job, status, or preferences I would encourage you to do your own research and consider the options. Privately paying permits the most privacy and no one would know about your attendance unless you tell them.