Well, maybe, sometimes, but most of the evidence suggests that it isn't really in our natures. What does seem to be in our natures is that we tend to organize into competing cliques, tribes, or gangs and struggle for supremacy.
The recent spate of world terrorism in the name of Islam has many questioning some of the central tenets of liberal democracy, especially the notion of tolerating and encouraging cultural diversity. In particular, tolerance can only work if it is truly mutual.
The new suspect in the latest Berlin massacre seems to have long been on the list of persons suspected of being involved with ISIS, and in fact was scheduled to be deported, and only wasn't because the security services couldn't figure out the paperwork or something. The CNN story on the subject suggested that the problem was very difficult since there were tens of thousands of suspects in Europe.
ISIS is clearly at war with the West, and in time of war civil liberties are nearly always curtailed. It might be time to summarily deport any aliens who can credibly be suspected of terrorism involvement. Angela Merkel's unilateral decision to let a million or so Muslim refugees into Europe was motivated by common decency, but it's likely to cost her her job. So far those refugees don't seem to have been a problem, but others, like the suspect, have.
The problem is not simply with those who enter Europe with evil intent. Being thrust into a foreign culture with sharply different laws and mores can be highly traumatic, and those not prepared to adapt can easily go off the rails. Legal immigrants from regions with sharply different customs should be required to prove they can adapt and deal with the local culture.