I think your dad is right. This depends on the state and some other factors, but it is likely that you were misclassified. This is extremely common, lots of big lawsuits about it right now in the context of gig jobs like Uber and Lyft where workers are also classified as independent contractors but really aren't.

Many states use a test that goes something like this:

(1) are the workers free from the control of the employer in providing a service?

(2) is the service not part of the usual business of the employer?

(3) is the individual part of their own independently established trade/occupation?

Sounds like by this test, you're clearly not an independent contractor and were probably misclassified. The question is, what remedy do you want?