strong case = strong argument

It means that it will be easy to support an argument for a topic. Ex: There is an argument about whether is was Jane or John who left the lights on. There is a video that shows John leaving the lights on. Someone could say, "There is a strong case to be made against John." because it is very easy to show that John was the one that left the lights on. This comes from the legal system. An argument in court is called a 'case'. A strong case is one that is hard to argue against -- it will stand up to the opposition's argument. When a person argues in court, it is called "making a case". So this just means they have a good argument.