You are confusing conservation of momentum with Newton's third law conservation of energy.
I'll go with a medium you understand,
YouTube
Notice how when the single moving ball in the Newton's cradle strikes the others it comes to almost a complete stop and conservation of moment is demonstrated by the free ball at the end beginning to move in the
same direction.
Ah yes, but don't forget that momentum was conserved in the
original collision (because the first ball comes to a stop).
It is not until the balls reach to top of their swing that any backwards motion is seen.
As an aside, the energy applied to the plane by the building in the collision is demonstrated by the destruction of the plane, and the reduction of the plane's remains velocity from several hundred miles per hour to zero in a couple of seconds.
Videos of 9:59AM do not depict this destruction to the ... plane ...
where the impact was said to have taken place, at the south
face of WTC 2.