Why do we need the MAC address if all Ethernet connections are done via IP address?

The MAC address is the hardware address, i.e. it is hard coded in the NIC of the machine. So it cannot be changed. Though all Ethernet communication happens via IP address, lower layers do not understand IP but they do understand MAC address. At the same time, there are instances when you use protocols other than IP, like IPX or AppleTalk. In such cases there has to be a mechanism which lets you work without changing hardware. So MAC addresses form the basic identifier of the hardware. MAC addresses are difficult to remember so we use IP addresses, which are more friendly, but not as friendly as names. Hope this clarifies.