Typically, the law does not require employers to offer any paid vacation days at all. However, once they do, employers must follow through on what they have promised. For example, they cannot take away vacation days as a disciplinary measure.
That being said, if you are an at-will employee (meaning you can be fired for any or no reason), you probably can be lawfully terminated for taking your vacation when the employer told you not to. In addition, your employer likely is free determine whether or not unused vacation days can be rolled over from one year to the next.
On the other hand, the above statements may not be true in your state. As with most employment issues, the laws governing vacation policies vary state-by-state, meaning you should contact an experienced employment attorney in your area for a more specific answer.
You can read more about employee rights at
https://www.workingnowandthen.com/.
This response is not legal advice, but is general information only, based upon the information stated in the question and general legal principles. It is provided for general educational purposes of the public who may have similar questions, not for any specific individual or circumstance. It is not intended to create an attorney-client relationship. Legal issues depend on all the specific facts of a situation, which are not present here. If you would like to obtain specific legal advice about your issue, you must contact a local attorney who is licensed to practice law in your state.