I can think of a couple of possibilities. By far the most likely in my opinion is that this is an LED (or possibly fluorescent) light with a regulator/power supply that's generating enough RF interference to make the television unable to decode the broadcast signal. You haven't had trouble with cable because the signal strength is higher with a cable than with an antenna (and it may also be in a different frequency band).
A second possibility, something of a long shot, is that the antenna booster amp and the light share a common poor ground and the booster isn't getting enough power when the light is on. If that were the case, I would expect the light to be also giving trouble and be dim.