If my employer gives us 6 paid holidays per year and Thanksgiving and Christmas day we are closed, don't they legally have to give us another day off during the week where there is a holiday?

The law does not require any paid holidays at all--it is completely voluntary on the part of the employer whether to do this or not. Since it is voluntary, it is up to the employer to decide how many paid holidays, what constitutes a paid holiday, etc. Therefore, no--your employer is not required to do that.