A full duplex walkie-talkie must transmit and receive at the same time. If there is the same at the distant end then there will be long distance acoustical feedback howling as the sounds go around and around.
A full duplex teleconference system uses a complicated digital echo-canceller circuit at each end that prevents sounds that are received from the distant end (and picked up by the local microphone) from being re-transmitted back.
In addition to the acoustic feedback problems highlighted by AG, there are considerable RF problems.
To transmit and receive at the same time using a small self contained transmitter and receiver, and presumably a single antenna, requires the use of two widely separated frequencies - one for transmit and one for receive.
Also, very good screening and filtering between the transmitter and receiver.
Cordless phones as well as GSM phones use time division multiplexing. Normally this requires some voice compression or at least store and forward where the voice is converted to digital then spit out as a shorter burst of higher data rate to be re-expanded at receiver end. The transmit and receive paths are given different time slots. Cellphones use different frequencies for receive and transmit primarily to avoid local interference from nearby base stations and other cellphone user and provide greater system capacity.
Old analog cellphones used real time frequency division multiplexing with a frequency duplexer to allow transmtting and receiving at the same time on different frequencies.
CDMA and WCDMA phones use frequency duplexers to transmit and receiver at the same time.