Given that we've reached that stage in the thread where we have to resort to repeating ourselves:
The door to the apartment was unlocked - known fact.
Therefore the apartment was not secure - known fact.
An abductor could gain access to the apartment without breaking and entering.
That's how it was possible.
And before I'm sniffily informed that I have not provided evidence of an abductor, well if you ask for a plausible, logical theory of abduction an abductor is somewhat of a pre-requisite to the theory.
So - a (theoretical) abductor (identity unknown) entered the unlocked apartment when he or she considered the risk of discovery to be at its lowest point during a window of opportunity (as confirmed as existing by the Met) and removed the child, for reasons unknown. During the (theroretical) abduction the (theoretical) abductor opened the window to the children's bedroom for reasons unknown. The (theoretical) abductor and Madeleine disappear into the night by means unknown, never to be seen again.
It's a theory short on detail and we can make up stuff to fill the gaps, but that's the bare bones of it. Plausible. Logical IMO.
Cue the chorus of indignation and cries of "it's totally illogical!!"