I've never understood why some rivers become the center of a nation or civilization while others are used as militarized demarcation lines. What characteristics differentiate the sorts of rivers that become population centers vs borders/defensive lines?
You have to understand that they often function as both.
Rivers are good to put towns nearby as they provide water, fish, and a means of trade and travel. Overland travel has typically been very difficult until relatively recently. If I'm to bring 100 barrels of wine to a nearby town, I could fit all of it on one boat with a rather small crew. If I'm to do the same by land then I'd need wagons, with teams of horses or oxen, with drivers to manage them. I'd need there to be a road, and even if there is one, I'd need it to be in decent condition.
As for borders - rivers are defensible. Crossing a river against an enemy is always a difficult prospect, moreso if you have animals or heavy equipment. Rivers are also quite evident, so there is no need to picture an imaginary line. Trade, immigrants, and invaders will usually have to come towards specific crossing points at bridges and fords and thus face defenders or at the very least men who can collect "tolls" for using the crossing.
Rivers are rarely 'decided' as borders or as population centers - they just tend to become borders, because of their defensibility.
For an example, look at the Rhine river. It is and has been packed full of towns, but it has also functioned as a border for centuries.