Why would a CNA program be free?

Because there's a huge shortage of CNAs, and healthcare facilities are desperate for them, so they're willing to pay for people to get certified. Why is there such a shortage? Because being a CNA is hard and often unpleasant work, and not many people are willing to do it. Of those who try it, many burn out and quit. Others do it temporarily, as a way to gain the patient care experience required for another line of work. It's hard for nursing homes, rehab facilities, etc. to find and keep CNAs, so many of them will pay for people to become certified.

No good reason. Are you sure you would qualify for licensing in your state? Better to consider your local community college for CNA program as that's where local hospitals, nursing homes, etc, are likely to recruit. And your state's community college system will have to meet state requirements for licensing.

You get what you pay for. "Free" is not worth much. Beware! Who is running this program? IF, for example, a hospital was running this program for the purpose of hiring graduates of its training program, then you could consider it. Otherwise, not.