Your insurance company will require privileged information be released to them before they will pay. In other words, by using your insurance, you give up your confidentiality (see #5).
Your insurance company will set limits on what kind of therapy you can have (or whether they will pay for it at all--see #3), how often you can come, and how long you can come. Some companies want prior authorization for the initial session, and periodic re-authorizations thereafter. This means that every so many sessions, it is possible that they will say, "No more!" This creates a chronic uncertainty that is antithetical to deepening the work of therapy.
Insurance will only pay for "medically necessary" treatment, meaning you will have to have a formal diagnosis of mental illness before they will even consider a claim. Medically necessary or not, some policies will not pay if the diagnosis is not severe enough (for example, they may not cover ADD), too severe (for example, addictions), or for treatments like marital therapy.
The biggest part of personal-growth-oriented psychotherapy occurs in the working relationship you and your therapist build together over time. Introducing a third party into the equation can and usually does disrupt that seriously.
If you and your therapist have always in the back of your minds that what you are saying/doing in treatment can be discussed with a so-called "care manager" from the insurance company, or that what you say or do can affect whether they will continue to pay for your treatment, then it puts everybody on guard. And we all know that letting down your guard, total honesty, is essential to successful psychotherapy.
If you decide to use your insurance, you must contact your insurance company ahead of time to find out if your therapist is on the provider panel, and whether the insurance policy covers the type of therapy you are considering for the type of problem you have. You must find out what the annual limits are, what your deductible is and whether you have met it, and what your copay will be for each session. There are too many different insurance companies selling too many different products for your therapist or her front office to be able to keep track.
You may be required to contact them, by the terms of your policy, in order to obtain prior authorization. If they are going to require periodic re-authorizations, you may be able to mitigate some of the interference with the therapeutic relationship by taking care of these yourself: Ask if they will let you do that.
If the therapist you have chosen is not on the panel, ask whether you have out-of-network benefits. You may still be able to use your insurance for treatment with the professional of your choosing.