That would be down to the notion a people can decide their own fate, and Artsakh, the highlight of the disputed area, has a predominantly Armenian population.
But it is officially Azeri territory, and breeding or migration dont warrant ownership and control of inhabited lands. However, it is easy to lose sight of simple truths, with outside forces fanning the flames of ethnic and religious differences. Hostile actions has been on-and-off.
But basically, since 1991 its been extreme conflict between Armenia and Azerbaijan. The dispute has been over the Nagorno-Karabakh region on their border, which contains the unrecognized Republic of Artsakh. The region was occupied by Armenia, after the dissolution of the USSR the Soviet Union. The UN Security Council has issued four resolutions calling for returning the lands to the Republic of Azerbaijan, in vain. Even Armenia hasnt accepted the independence of the disputed area. Rather, it wants the Azerbaijani area annexed to Armenia. In the meantime Turkey intends to pit one tribe against another, by dispatching Azeri and Turkish forces to the conflict zone. Iran however, believes this war also to be a religious war by nature.