Why adhesives almost always fail at the surface
Why the bond between glue and material is weaker than the glue itself.
A glued joint that comes apart almost never fails because the cured glue in the middle of the joint tore in half, it fails because the thin boundary where the glue meets the material gave way first, since that interface is held together by weaker forces than the ones holding the glue's own molecules to each other.
What is really going on
Inside a fully cured adhesive, whether it set by drying or by a chemical reaction, the molecules are joined to their neighbours by strong, direct chemical bonds, which is why a solid block of cured epoxy is genuinely hard to break apart by pulling on it. The bond between that same epoxy and the wood, metal or plastic it is stuck to relies on a different and generally much weaker kind of attraction, forces acting only across the last few molecules at the boundary, which depend entirely on how closely and completely the liquid glue managed to make contact with the surface before it hardened. Wetting describes exactly this: whether a liquid spreads out to touch a surface intimately or beads up and only makes contact at a few high points, and how well a glue wets a surface depends on the surface energy of the material underneath it. A low-energy surface, however clean, only lets the glue touch a fraction of the area it appears to cover, and any point where true contact was never made is a point with no bond at all, waiting to be the place the joint starts to separate. Contamination makes the same problem worse without changing the material underneath at all, since a film of oil, dust or old wax sitting on an otherwise high-energy surface behaves, as far as the glue is concerned, like a low-energy surface in its own right, intercepting contact before the adhesive ever reaches the material it was meant to bond to.
The sticker comparison
Peeling an old label or sticker off a glass jar shows exactly where the weakest link usually sits. The label almost always comes away cleanly, lifting off the glass in one piece with the adhesive layer still attached to the paper, rather than tearing through the middle of the paper itself, because the bond between the adhesive and the glass beneath it is the weakest part of the whole arrangement, weaker than the paper, weaker than the adhesive layer's own internal strength, and weaker than the bond between the adhesive and the paper backing it started life stuck to. Deliberately tearing the label itself, rather than peeling it, takes considerably more effort and force than lifting it cleanly away at the glass, which is a fair demonstration of how much stronger the material and the bulk adhesive both are compared with the interface where they meet the surface underneath.
The one number worth remembering
The covalent bonds holding a cured epoxy's own molecules together are strong enough that the bulk material can rival the strength of some metals and plastics it is used to join, but the attraction between that same epoxy and a surface it merely touches, without any chemical bond forming to the material itself, can be many times weaker, which is why the practical strength of most glued joints has far more to do with how thoroughly the surface was prepared and wetted than with which adhesive was chosen.
Where this stops being true
Because failure almost always starts at the interface rather than inside the glue, the single most effective way to strengthen a glued joint is not switching to a stronger adhesive, it is improving how well the existing adhesive can wet and grip the surface, by cleaning away oil, dust and old finish, by roughening a smooth surface to give the glue more area and more places to key into mechanically, and by choosing a glue whose chemistry actually suits the surface energy of the material being joined rather than assuming any adhesive will do provided it is strong once cured. A joint that fails soon after gluing, rather than under genuine load much later, is nearly always telling a story about the surface it was applied to rather than about the adhesive that was chosen, and inspecting the failed faces, checking whether the fracture ran cleanly along the interface or tore through the glue itself, is usually enough to say which of the two actually happened.