War is a pretty big part of human history. It might seem like it happened more in Europe because that might be where a lot of history in primary schools focuses, but there have been significant and frequent conflicts just about everywhere else in the world.

Just using the medieval period as an example (say, 500 AD to about 1500 AD) there was the war of conquest waged by the Islamic Caliphate across not just the Arabian peninsula and the Middle East, but also into parts of Asia Minor, across North Africa and up well into Spain. Beyond this conquest, the Muslim world would continue to clash with the Orthodox Christian world as far as 1453 AD, when Constantinople fell.

Also during this era was the conquest by Ghenghis Khan. By 1270 AD, the Khan's empire spanned larger than any empire before or since (in terms of square mileage) from east China all the way into parts of eastern Europe. Something like that doesn't come without a significant amount of warring!

In short, "it just seems that way."

There have been plenty of questions recently about warfare in pre-Colombian Americas. They provide some good sources for the northern bits. As for warfare in South America, I've done a good bit of research and reading on it. I can reccomend Charles Stanish and Elizabeth Arkush's article here that critiques the "peaceful history" perspective you share with many scholars. Arkush has a number of other excellent writings on warfare around 1000-1200 AD around Lake Titicaca, focusing on large fortified settlements called "pukaras." For work on warfare in the central Andes, check out Tiffany Tung's work on violence in the Wari empire, the first expansive "state" in the region. The site I work at belongs to the Recuay tradition, a period of frequent warfare, contemporaneous with the coastal Moche. From these cultures we see both imagery of warfare and highly fortified settlements.