The main reason why it is acceptable for human beings to interfere with the environment (or with the various ecosystems that make up the environment) is the fact that all human activities inevitably interfere with the environment. Human beings cannot possibly live without interfering with the environment.
We may think that human beings once lived without interfering with the environment. In the days before machinery and industry, surely we lived without interfering with the environment. But this is simply not true. There is strong evidence to suggest that even very primitive human beings interfered with the environment. For example, when the first humans entered the Americas and Australia, they caused the extinction of many species that they hunted. Even such primitive peoples with very little technology interfered with the environment. Therefore, there is no way that people (particularly given how many people live on Earth today) can live without interfering with the environment.
The trick, of course, is for us to interfere with the environment as little as we can. We need to find ways to, for example, use fewer chemicals in our agriculture and less energy in our daily lives. We will never stop interfering with the environment, but we can limit our impact if we try hard enough.