Every spring a war captive of superior physical beauty was chosen to impersonate the god Tezcatlipoca (Smoking Mirror).
Worshipped like a deity, the captive was adorned in precious clothing and given wives and servants in a yearlong rite that culminated in his sacrifice to the god.
The "Festival of Toxcatl" is one example. We consider this practice strange, even repellent, but it has nothing to do with barbaric bloodlust. The Aztecs had elaborate mythological beliefs that required human sacrifice.
Demonstrating their sincerity, they also practiced bloodletting on themselves. Again, this is because the gods demanded it. They didn't want to make bloody spectacles of themselves, they had to do it.
Killing people irrationally
In my mind, it's not much different from our modern practice of bombing villages in Vietnam or Iraq. There's no rational foundation to believe these countries threatened the US, yet we bombed them without regard for civilian deaths. The people who did the killing had an irrational, quasi-religious faith that what they were doing was God's will. That it would bring peace and prosperity to their homeland.
Well, the Aztecs also believed that killing people would bring peace and prosperity to their homeland.
In one place, the exhibit links human sacrifice with state-sponsored terrorism, but it doesn't elaborate. Even that is couched in terms of appeasing a war god, I believe. I don't think there's any case where the Aztecs simply said, "No god has ordered us to sacrifice this person. There's no religious justification for killing him. We're doing it for secular reasons: to frighten our enemies, and because we like it."
For more on human sacrifice, see Human Sacrifice "Prevalent" Among Indians? and Were the Aztecs Murdering "Animals"? For more on the exhibit, see Divinities in Aztec Pantheon and Confrontational Aztec and Roman Art.