Being denied Social Security disability does not necessarily preclude the receipt of unemployment benefits. Social Security disability is a federal program, and unemployment is a state program.
You need to contact your state unemployment agency to find out why you are not eligible for benefits. In Michigan, an employee must be terminated or laid-off to be eligible for unemployment, and the employee must have worked for the employer for at least 90 days.
On the flip side of your question, drawing unemployment usually requires affirming that you are "ready and able" to work, which is contrary to a claim for disability (unable to work for at least 12 months).