And you try to think about the fact that, perhaps, a person "suffers from diseases and dies from cancer" precisely because he eats meat, fish, milk and eggs. A monkey understands that it is a species food for it, but a person, unfortunately, not always.
Read "The Chinese study" by K. Campbell
And you, in fact, what kind of monkey do you mean, speaking about the closest relative of man? However, not a single one can do without milk, primates are mammals.
For example, chimpanzees are an omnivorous species, they feed on both fruits and insects, bird eggs, crustaceans, rodents and ... fellows (monkeys, for example ). For hunting, they use improvised means and even make primitive weapons. Animal protein is an indispensable component of the diet of many primates.
There are completely carnivorous primates, but they are not as close relatives to us as chimpanzees.
All animals in the wild suffer from many diseases they suffer from diseases much more strongly and the lifespan of wild animals is, on average, two times less than that of the same animals tamed by man. Circus chimpanzees live much longer than their wild counterparts and sometimes die of cancer.
If we talk about cancer, monkeys and even completely herbivorous cows get sick with it, if they live to such an age when immunity ceases to cope with the appearance of malignant cells.