There are a number of arguments that can be made against this idea. Let us look at two of the most important of these.
First, there is the argument that violent behavior existed long before television or other things like violent video games ever did. Even decades ago, when there was much less graphic violence on television and in movies (and when there were no video games of any sort) there were plenty of people acting in violent ways. This seems to rebut the idea that people come to act in violent ways because they view violent behavior and actions in the media.
Second, there is the argument that it is simply impossible to isolate and identify the specific impact of viewing violence in the media. For one thing, there is no way to accurately quantify how much violence each person sees in the media. We do not know what individuals watch, how much they pay attention to it, or how they feel about it. We therefore cannot look at individuals who commit violent acts and then determine how much violence they saw in the media. Just as importantly, we cannot accurately compare them to other people who watched the same amount of violence. We cannot accurately divide people up based on how much violence they have consumed and then compare the extent to which they act violently.
For another thing, even if we could accurately measure how much violence people see and how violent they are, we would have a very hard time filtering out other influences on them. We would, for example, have a hard time figuring out how much of their violence comes from the media and how much from the way in which they were parented. Human behavior is affected by a multiplicity of factors and it is exceedingly difficult to tease out the specific impacts of any one of those factors.