Why is an X-ray not good for back pain?

Looks at bone only. Xrays show only bone. A fracture is an unlikely cause of back pain. There can be several reasons for back pain, like lumbar disc inflammation with or without nerve impingment, facet joint irritation, sacroiliac joint irritation, muscle strain. A thorough physical exam and diagnostic studies will help determine what treatment will be best depending on your diagnosis.
Xrays for back pain. X-rays are excellent for seeing bones but don't image the disks well. Most people with back pain of less than 6 weeks duration don't require xrays because they will get better with time alone. An MRI which is very expensive is the test of choice if needed because it can visualize the culprits: pinched nerve roots and disks with accuracy. It should be reserved for intractable symptoms.
It is useful. for looking at the bones and assessing for fractures or degenerative arthritis, but standard xrays don't visualize soft tissue structures such as disks or muscle, and even the evaluation of bone is not as detailed as CT or MRI, so many potential causes of back pain would simply be invisible on x-ray.