However the point about slavery not being a genocide is correct if going by the true definition used in education and human rights groups.
There is no single or 'true' definition of genocide. It's evolved over time. The most recent authoritative legal definition is from the statute of the International Criminal Court, and this is what many people use today:
For the purpose of this Statute, "genocide" means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnic, racial or religious group, as such:
(a) Killing members of the group;
(b) Causing serious bodily or mental harm to members of the group;
(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
(d) Imposing measures intended to prevent births within the group;
(e) Forcibly transferring children of the group to another group.
Imagine saying there wasn't an Armenian genocide because there's so many damn Armenians around, or the Holocaust wasn't a genocide because, well you get the picture. It's ridiculous.