You have a high deductible
If you have an insurance plan with a high deductible, you will need to pay out of pocket costs before your insurance will cover an in-network provider. This can sometimes be thousands of dollars before your copay applies.
Privacy
Insurance companies request access to information about your therapy and perform regular audits. They can control the number of sessions, type of therapy, or length of treatment.
Accessibility
Insurance companies can decide not to accept your provider based on the area being "oversaturated" with therapists. This means that a therapist who is a great fit for you may not be in your insurance network. As a client, this means your options are limited, especially if you are looking for a specialist in a particular area.
Quality of Care
Therapists who do not participate with insurance companies have freedom in how they practice and often have a smaller number of clients, which can allow them to provide higher quality care to each person. There is also no limit to the time you can be in therapy or the kinds of issues you can work on.