The predecessor to the A340 program begun in 1982, when Airbus released the first specification of the designated TA9 and TA11 programmes and in 1986 the TA9/TA11 programmes were officially launched as the A330 and A340 development programmes. By 1986 Airbus, with their 310 aircrafts, as well as Boeing, with their 757/767 aircrafts, already had twin-jets flying under the ETOPS90 and ETOPS120 rule, introduced in 1985. Meanwhile Boeing presented the predecessor to the 777 programme, the 767-X ("enlarged" 767) in 1986, but due to customer demand launched the clean sheet 777 twin-jet programme in 1988.
Reading up on that history, I wonder why Airbus did not opt to redesign the A340 with two engines, rather than four. I judge, that by the mid-80ies, the feasability of two engines for a widebody long-range aircraft with more than 300 passenger was already clear. The loosened ETOPS rules meant, that even regulators were paving the way for such an aircraft.
What was to rationale of Airbus to develop the A340 into a four-engine airliner, while at the same time, Boeing was developing the 777 as a two-engine airliner?
EDIT: I found another question and answer, which states that ETOPS was the reason. But ETOPS rules were introduced in 1985, while A340 development programme was launched in 1986. So Airbus made a decision despite being ETOPS already in place.