Why would they build a city below sea level? Did the founders of the city not realize what they were doing, or did they just not care?
It was just about the only piece of solid ground anywhere close to the mouth of the Mississippi. You can read about its history here.
There’s also the point that the land in that area is slowly sinking due to the accumulation of billons of tons of sediment brought down by the Mississippi River. In ancient times, sediment would be continually deposited by annual floods, buidling new land on top of what was subsiding.
But once buildings are present, people don’t care for the flooding and they tend to build levees to control it. This causes the sediment to wash out into the Gulf, rather than be spread over the land. Of course, the river bottom does receive sediment, so you have to keep dredging the river and raising the levees. The Mississippi now (well, 2 days ago) flows well above the level of the land - a rather obvious long-term danger.
Another significant danger is the impending “capture” of the Mississippi by the Atchafalaya River, just to the west. This would have happened already without many billions of dams, levees, dredging, etc. It’s not impossible that it will happen soon, leaving New Orleans without a river.
For a fascinating discussion of this, see the book The Control of Nature by John McPhee.
Bingo. You can’t get no better.