There are a variety of ways in which one can answer this question. Let us look at two of them.
First, we can ask why it is important to address the environmental issues raised by the use of plastics in packaging. The main reason for this is because this use of plastics can help to cause a number of environmental problems. For example, we know that a large amount of plastic that is used in packaging ends up in the ocean. Some of this plastic ends up in a huge swirl of garbage in the North Pacific. This plastic ends up harming various kinds of wildlife and even human beings. It harms wildlife like turtles and large birds because it fills up their stomachs and leaves them unable to hold enough real food to live on. It hurts humans because the toxins from plastics are ingested by creatures low in the food chain. The toxins move up the food chain, eventually getting into fish that humans eat. In short, then, it is important to address these issues because they are very serious environmental issues.
Second, we can ask why it is our responsibility to address these issues. In other words, why should we feel that we are the ones who need to do something about these problems? The main reason for this is that we are the ones who consume the things that are packaged in the plastics. If we cause the plastics to become part of the solid waste stream, we are the ones who need to get it out of that stream. In addition, we are the ones with the power to do something. Companies will respond if their customers demand that less plastic be used in packaging. Since we are the customers, we have the power to push companies to reduce the use of plastics.
Thus, it is our responsibility to address these issues because they are serious issues that come about because of us and which we have the power to remedy.