I believe it's the last one: Europe's system of military alliances enlarged small conflicts. There were a lot of alliances between different European countries at the time, and if you messed with one country, chances are that you got that country's ally involved too...which makes for wars pretty fast.
This policy is known as the Monroe Doctrine. This doctrine was an essential part of American thinking that was born from a paranoia that European influence would become pervasive in the Americas.
