Take a piece of metal wire and pull on both ends -- if you pull hard enough it will stretch imperceptibly, but you will have a very hard time breaking even a thin guage wire with your bare hands. Now if you take the same thin guage wire and push the two ends together you will have no trouble at all because it will buckle under the smallest compressive load.

Compressive strength is identical to tensile strength, as long as buckling isn't an issue. For example, a short thick block of metal will stretch or compress by the same amount if the same load is applied in tension or compression. Your calculation for compressive loading is only valid for short thick blocks of metal.

There is a ratio of length-to-diameter when buckling becomes a problem. Getting into the math isn't the point, just think about the first paragraph above. Your lunar tower will require guy wires to support it.