Eating ice can be bad for your health in two ways. First, and most obvious, is that eating ice- if you crunch it instead of sucking on it- can damage your teeth. My sister, who suffers from iron deficiency/ anemia, has eaten ice since she hit puberty. Now, at 39 she has cracked, broken and lost several teeth as a result of the behavior. Dental health is an important part of good overall health.
The second reason eating ice can be bad for your health is because eating ice is a bad substitute for treating whatever problem is causing the urge to eat ice. The problem could be pica, anemia or a vitamin or mineral deficiency. Most people who crunch ice do not address the underlying issue that causes the craving.