Having disability insurance can set your mind at ease, especially if you have both private disability insurance in combination with eligibility to file for a state or federal disability program like Social Security Disability. However, once you do file a claim, it's not unusual for insurers, including SSDI, to reject your claim. People often wonder if applying for both SSDI and a private claim can result in only one claim being accepted, but that's not the case. If you were rejected, the rejection likely has to do with a very different reason.
Receiving disability support from a claim filed with private insurance should not make you ineligible for support from Social Security Disability Insurance. SSDI is a public program that people can apply to regardless of current job type (though they do have to have a work history overall), while you're also eligible to file a claim with a private disability policy if you are a policy holder. Eligibility doesn't mean automatice acceptance of your claim, however.
Level of Disability
One possible reason for SSDI rejecting your claim while private insurance accepted it is that you did not prove, to SSDI's satisfaction, that the level of disability is permanent. SSDI is meant to help with permanent disability, where you can no longer do the duties of your old job and accommodations aren't possible. Private insurance is different; that can cover disability that is not permanent. For example, if you're going to be out of work due to your condition for a few months, and you can't work even with accommodations until you heal -- but you should heal within those few months -- then private disability insurance companies could approve your claim while SSDI denies it.
Who Claimed You Were Disabled?
The medical exams that form the basis of your applications could be another sticking point. It's possible that SSDI (or your private insurance company) didn't agree with what the doctor decided. This can be a difficult situation as your private insurance company may have made you see a particular doctor instead of your own (so you're not familiar with how good that doctor is, or if the doctor misdiagnosed you as having a temporary disability instead of permanent).
A denial by either SSDI, a private company, or both isn't the end of the road. Should you be denied, you can begin the appeals process. However, you need a lawyer to help you through the process because your application for an appeal has to follow guidelines exactly. You risk a second denial otherwise. And these appeals can take a long time -- you want to get an acceptance as soon as possible.