I know that iron is extracted from its ore (e.g. haematite) in a blast furnace. However, why isn‘t copper extracted from its ore using a blast furnace?
because most iron ore is iron combined with oxygen or sulfide. heating to melting produces pig iron which can be further refined to make steel or cast iron. the primary ore of copper is a mineral that is a combination of copper and iron. so just heating does nothing to purify either metal. relatively pure copper is obtained by smelting with lime which causes the iron to form an oxide slag which can be floated off, leaving the copper blister behind. the metallurgical term for both processes is smelting.
Iron ore is usually an oxide. It is a rather strong bond with the oxygen and it takes energy to split the bond and release the iron. Copper is not as active as iron and can be found free in nature. In copper mines, you get copper, it does not need to be separated from its ore.