I cannot count the times people cite "it's the cycle of life!" when declaring the inevitability of animals (humans usually included) killing other animals (humans usually not included). There is an iota of truth to the statement, alas I find this to be an oversimplification that is used to dismiss the agency of humans as individuals, and as a species in how our actions affect the health of our planet.
Context is everything, and my parenthetical additions to "it's the cycle of life" above highlight the primary nuances, I believe, so let's start there.
Generally, most ethical stances would exclude humans killing humans as something good. War (when it includes state sanctioned homicide) murder, cannibalism, even self-defense (when non-lethal means are possible) are generally recognized as not applicable to the "cycle of life" forgiveness mantra.
Next, let's consider non-human animals killing humans. Here, most will agree our species gets a pass on being the object of carnivorous animal attacks or the spread of bacteria and viral vectors by other animals (mosquitos carrying disease, rabid animals carrying disease). Humans take for granted that they are not involved in the cycle of life in these cases and taking every precaution and action to prevent human death is our implicit duty. Frankly, no matter what the killer is (animals, plant-based poison, gravity, extreme weather, or even time) we tend to take the stance that if human death or injury can be prevented, humans should take action to do so.
Of course other things are killed than just humans, and this non-human animals killing other non-human animals is what most people intend when using the "it's the cycle of life" comment, but each situation really deserves a closer look if our true intent is to preserve a healthy planet.
Predation obviously does occur, and has occurred for billions of years in the biomes of Earth. For organisms (plant, animal and bacterial) that get their nutrients from anything but raw minerals in the soil, water and air, or organisms that have perished from random forces, taking the life of other organisms is necessary if their own lives and their ability to propagate are to be protected.
Our living planet does seem to incorporate a complex food web for all the many varied organisms to coexist and over large spans of time to coevolve. As such, life does have a cycle that feels miraculous if only because we cannot comprehend the billions of years over which our planet's dynamic system has come about...that is until human intervention has turned into a powerhouse.
Take humans out of the equation and there is by and large a balance in Nature. Predating wolves, lions and coyotes, etc. hunt and kill mice, rabbits and deer. When one of the predating species gets too numerous their prey species take a downfall and subsequently so will the predating species. Generally, this will keep populations in check, which is an important part of "the cycle of life."
Again, humans are the exception. Because they have refined methods for killing others and for healing themselves, over the past several thousand years, the population of humanity has grown exponentially. Our population is projected to grow from its current 8.2 billion and top off around 10 or 11 billion in the next century or so.
Because of this massive presence on the planet we are doing disproportionate damage to self-repairing, biodiverse, global systems. The massive development of human infrastructure (factory farming of food and companion animals, agricultural sprawl, alteration of atmosphere, alteration of water systems, etc. etc.) has a devastating effect on the long term status of the global environment's health.
Which is to say, human choices to regulate our population size and our per capita impact on natural systems will continue to have a critical impact on the world we live in unless we adjust our civilization's mindset.
In conclusion, "It's the cycle of life," does not excuse us when our human actions lead to the unnecessary killing of animals. We do not need to kill animals to thrive as a species. If our companion animals are killing wild-animals then the fault is ours as well. Humanity has become a presence which is inherently unnatural, and we should own that status, so that we can be proper caretakers of a beautiful world with longevity for the good of all species.
The next time you say "it's the cycle of life" ask yourself what can you do to make the natural cycle more resilient, and thriving in spite of human hegemony. Ending human hunting and fishing, eliminating unnecessary human initiated animal breeding, restraining our animal companions, going vegan, reducing overall consumption in general, etc. We humans are not controlled by Nature, so we have to make better decisions and actions if we want to keep our shared planet healthy!