How does genocide go against human rights? 

One of the most basic human rights is the right to live and a government has a duty to protect the lives of its people.

In other words, it should not harm people because of their religious beliefs, race, or any other attributes about them.

Now, when a nation does not value its people's right to live, tensions start growing really fast and lives are at risk. A perfect example of this was during World War II when the Nazi government killed nearly 6 million Jews which we know as the holocaust which is a systematic way of killing a group. In addition, there were about 1.5 million Armenians that died in the early 1900s when they were targeted by the government of Turkey. Both of these examples are genocides that violate the right to live and also other rights as well such as freedom of torture, rights to basic needs, etc...