That's a good question. I will turn it around and ask you, "Why aren't humans turning into monkeys right now?"

The reason that neither is turning into each other is because both groups (humans and the various species of monkeys) evolved on earth from a universal common ancestor, about 3.7 billion years ago. Over time, evolution (change over time in characteristics that are inheritable from parents) drove the formation of various species. Some of those species have further sub-divided into more species, while others have gone extinct, and others have remained more or less the same for millions of years. Nonetheless, all living species today have evolved over the same amount of time from that initial point. The order primates (of which monkeys and humans are both a part of) go back at least 65 million years. About 40 million years ago, the infraorder Simiiformes (which includes Old World and New World monkeys, and Old World apes - including humans). Currently, there are over 230 species of monkeys (both Old and New World); 17 "lesser ape" species (gibbons), and 7 "great ape" species, including people.