“...how does this happen at an ecumenical council...”
None of the documents of Vatican II explicitly state the intent to define Faith and Morals.
Solemn dogmatic definitions are required for infallibility and this was not done at Vatican II.
The Council was pastoral in nature and not dogmatic.
It was a terrible idea to call a Pastoral Council at that time and important Vatican II documents are purposely ambiguous and sow the seed of discord that is bearing bad fruit to this day. It is this discord that comes from the fallen dark side; the confusion in and itself does not end with the premise: therefore the Pope is not a Pope.
“...the Council ... avoided proclaiming in an extraordinary manner dogmas endowed with the note of infallibility” as per Pope VI’s statement on January 12, 1966.
Here's the whole quote:
"In view of the pastoral nature of the Council, it avoided proclaiming in an extraordinary manner any dogma carrying the mark of infallibility, but it [Vatican II] nevertheless endowed its teachings with the authority of the supreme ordinary magisterium, which ordinary (and therefore obviously authentic) magisterium must be docilely and sincerely received by all the faithful, according to the mind of the Council regarding the nature and scope of the respective documents."
The Supreme Ordinary Magisterium (separate from the Extraordinary Magisterium) is the Universal Ordinary Magisterium and it is (supposed to be) infallible. So we still have the issue of an ecumenical council contradicting previous Magisterium in matters of faith and morals.