The legacy of 10Mbit twisted-pair Ethernet is just two pairs, at RJ45 pins 1+2 and 3+6. These already allow for full duplex operation, provided that the active elements support it. This wiring has been inherited by 100Base-TX.
Half-duplex operation is inherent to coax media (10Base-2), where full duplex is not possible at all.
Twisted pair Ethernet (10/100 Mbps), by virtue of having one pair in each direction, is inherently capable of full duplex. But, the old active element, called a hub (a dumb electrical repeater/amplifier) turns the network into a multi-exit half-duplex medium - not capable of full duplex. To make use of full duplex on twisted pair media, you need the network to contain a "non-blocking data stream cross-connect element" in the active element role = you need a bridge/switch. I'd almost say packet-level "store and forward", except that the other mode is "cut-through switching", which is also compatible with L1 full duplex operation. A special case is a point-to-point twisted pair connection (no hub/switch) that is also inherently full duplex capable.
I.e. the 10/100 metallic media, albeit twisted pair, with two independent pairs, is still capable of running in half duplex, for various legacy-compatibility reasons. The PHY transceivers are still capable of running the CSMA-CD over twisted pair.
Gigabit Ethernet over metallic wiring is running over all 4 pairs, using full duplex and echo cancelation on each pair. Just the initial auto-negotiation handshake still runs over the two pairs: 1+2 and 3+6. Thus, if you have a broken patch-cord, where only 1+2 and 3+6 are functional, and you use it to connect two gigabit PHY ports, the link handshakes at 1 Gbps, but then fails to function...
If auto-negotiation fails, the fallback mode is the lowest rate at half duplex, i.e. typically 10/half.