Is plate tectonics a hoax theory? How can tightly packed plates move?
tectonic plates are not completely rigid they can bend, flex, and in the case of oceanic plate, get pushed under each other and melted back down.The plates move by sliding under each other, melting, or bending 

Take a toffee-bar candy, hang most of it off the side of a table and put something heavy on the other end to hold it in place, wait a few hours, just under its own weight it will bend 90 degrees. However bend it fast by only a few degrees and it will snap. Rock behaves in a similar fashion, do it slowly enough and with enough force and you can bend it. Basically all solids behave like this to a certain extent. tectonic plates are not rigid on the large scale.

bending rock leaves behind traces like this and this

bend it to fast and the rock breaks creating a fault lines like this and this 

plates pushed down get remelted, it helps if you think of oceanic crust as exposed mantle that has been cooled into a solid, while continental crust is much less dense and sort of floats on top of the more liquid mantle. that's why continental crust does not subduct but oceanic does. In essence there are huge gaps between the the permanent plate material, it just cools when exposed forming a hard surface skin called an oceanic plate.



we can even see that in how earth quakes behave around subduction zones getting deeper and deeper in the direction of movement until the stop indicating where there are no solids left to break. 

here is an earthquake depth map for japan. notice how they get deeper in the direction of the movement of the pacific plate (west by NW) as it dives under japan. 

If you look at a global map of plate movement you will notice that at then end of a moving plate (in the direction of movement) is either a mountain range or a subduction zone, or often both.