It's just a crazy good return on investment if I take my 400 Hammer army and go capture 4000 Hammers worth of stuff. That's the temptation of war. It's always been the temptation of war.
You can avoid or bypass war and still cruise to victory. The AI won't attack unless they feel they outclass your military dramatically or, now, Grievances have stacked up; they might scowl at you but they won't attack unless it's an expected curbstomping. Build enough units so that no neighbors in the vicinity have twice your military score, and check your military score often! On higher levels the AI starts with more than twice your military strength so get to work making units.
When conducting a trade, and you get to the max they will give or take, overpay or give them a kickback so they think it's a favorable deal. Give them a fat payment/bribe and call it Foreign Aid; it's the only reason why any nations pretend to like the US and are willing to take our phone calls. Get that embassy in there right away and, if you can, try to have your first meeting occur with a non-threatening unit; the best Scout in the game is a Monumentality Builder with one charge left.
There are ways to exploit the AI's aggression too. Get God of War pantheon and taunt them into attacking within 8 hexes of your Holy Site (or theirs); it can amount to an enormous pile of Faith and you also know where the archeological sites will be in the future. Two Archers in an Encampment and a walled city can hold off just about any assault, and be Level 3 at the end of it.