Printed parts snap along the layers
Why a printed part is strong in two directions and weak in the third.
A printed part is weakest between its layers, because each layer is only fixed to the one below it by however well the hot plastic managed to re-melt the surface it landed on, while the plastic within a single layer is one continuous, unbroken strand, so a break running across a layer has to tear through solid material and a break running between layers only has to separate a bond.
The mechanism behind layer adhesion
Within a single printed layer, the nozzle lays down one continuous strand of plastic that never stops flowing as it turns corners, so the material along that path is as unbroken as a single piece of plastic can be. Between one layer and the next, there is no continuous strand at all, only the hot plastic of the new layer meeting the already-cooling surface of the layer beneath it, and however well that reheats and re-melts the top of the layer below, the bond it forms is never as complete as a strand that was never separated in the first place. Pulling a part apart within a layer means tearing through that continuous strand, while pulling it apart between two layers only means separating two surfaces that were never one piece of plastic to begin with. How completely those two surfaces fuse depends on how hot the new layer still is and how long it stays in contact with the one below, which is why a part printed too fast, with each layer cooling before the next one arrives, snaps between its layers even more easily than one printed slowly enough to let each new layer properly re-melt the surface underneath it.
The sandwich-biscuit comparison
Twisting a cream-filled sandwich biscuit apart shows how much weaker a stuck-together join is than the solid material either side of it. A single biscuit, bent directly, takes real force to snap and breaks unevenly across its own body. The same biscuit, twisted at the cream layer where two separate wafers were pressed together rather than baked as one piece, comes apart with barely any effort, cleaving exactly along the join and leaving both wafers intact. A printed part behaves the same way: forces that try to bend or snap it within a layer meet the equivalent of the solid biscuit, and forces that try to peel one layer from the next meet the equivalent of the cream, a join rather than a single continuous piece of material. Nobody twisting a biscuit apart is surprised by how little effort it takes, because the cream was never pretending to be as strong as the biscuit either side of it, and a printed part's layer joints deserve exactly the same lack of surprise.
The number that matters here
A joint between two printed layers can hold well under half the strength of the plastic within a layer, so a bracket that comfortably survives being bent side to side, loading it across its layers, can snap with surprisingly little force if the same load instead tries to peel one layer away from the next along the direction the part was built.
Where this stops being true
Printing a part on its side rather than flat changes which direction the weak layer joints face relative to the load it will actually carry, and a part redesigned so the load pulls along the layers rather than between them can be made from the same plastic on the same printer and still end up many times stronger, because the weakness was never in the material, only in which direction it happened to be asked to resist. A small hook or bracket, printed standing upright so the pull runs along its layers rather than trying to peel them apart, can survive a snatch that would snap the same shape printed flat on its back without any change to the plastic, the settings, or the design itself, only the orientation it was built in.