There are certainly many examples we can find of how humans compete with other animals for natural resources. This type of competition is common between many animal species, not just humans against other animals.
One example is fishing and how we compete with other animals for those fish. Fish is a major food source in many places around the world and is very valuable as a source of nutrition for humans and other animals. In some cases, animals have been going hungry as a result of humans overfishing. When humans overfish, there is a smaller food supply for bigger fish, sharks, whales, birds, and other animals. Those animals are competition for humans too because they are fighting for those same fish in order to survive.
An example is interspecific competition between animals such as the lions and cheetah species for food, i.e antellopes