Full-duplex and half-duplex have nothing to do with monologue versus dialogue.
Full-duplex versus half-duplex is only stating whether both sides can transmit at the same time. Or whether only one can transmit, and the other has to wait until the first one is finished, and then it is his turn to transmit. When we talk about full/half duplex it is almost always about a point-to-point circuit.
So it is not whether you can send in both directions. It is only about the *time* you can send. All the time both can send (full) or they have to wait turns (half).
For the record, there are also circuits where you can send in only one-direction. A satellite link would be an example. An MPLS tunnel would be another. In that case we don't talk about duplex. In that case we call it a "uni-directional link".
Bringing in TCP and UDP into this discussion is only confusing. They have very little to do with full versus half duplex. And even if you want to put that label on it: both TCP and UDP are full-duplex, because both sides can send at the same time (if they want to).
Even mentioning that TCP and UDP can run over full- and half-duplex links makes hardly sense. TCP and UDP run on top of IP. And IP can run on anything. Fiber, 33.6Kbps modems, satellite links, wireless. Anything and everything. And it doesn't matter whether the underlying layer-2 technology is full- or half-duplex.
Small history lesson.

25 years ago someone made a joke about that.
He wore a t-shirt to a convention that said: "I P on everything".
Bonus points if you know who this guy is.