Before trying to really thoroughly comprehend movement, we should simply accept that it's measurement is relative to the scale we choose.
It's a strange claim by the way, because everytime we reach the door we have proven to be able to cover all these infinite halfway points all the way up to the door, regardless of the scale you choose before you start.
The actual movement is still happening, the trouble Zeno seems to have had with it, was accepting 1 scale-size on which you base your measurements of distance and movement. Infinity doesn't matter when it comes to reaching the destination, it does matter for comprehending distance covered,
Cheers