How do insects breathe, and why can't they get very big?
Insects have no lungs and no oxygen-carrying blood. They breathe through a network of tubes that delivers air directly to their tissues — and that system, elegant at small scale, is what limits their size.
The tracheal system. Air enters through spiracles, small openings along the sides of the body that can be opened and closed. From there it travels through progressively branching tubes — tracheae, then finer tracheoles — that end directly against the cells. Oxygen diffuses the last short distance straight into the tissue.
No blood transport is involved. Insect blood, haemolymph, circulates nutrients and hormones but plays little role in oxygen delivery. This is a fundamentally different design from vertebrates, where lungs load oxygen onto haemoglobin and the heart pumps it everywhere.
Why it is efficient at small size. Delivery is direct, with no intermediary. Some insects also ventilate actively by pumping the abdomen, and larger or highly active species have air sacs.
Why it caps body size. The system depends substantially on diffusion, and diffusion is only fast over short distances — the time it takes scales with the square of the distance. Doubling body size more than doubles the delivery problem. Tracheal tubes must also get proportionally larger and more numerous, taking up an increasing fraction of the body, and in the largest insects they begin to crowd out other tissue, particularly in the legs.
The Carboniferous evidence. Around 300 million years ago, dragonfly relatives had wingspans approaching two thirds of a metre. Atmospheric oxygen concentration was substantially higher then, which allowed diffusion to supply larger bodies. As oxygen fell, giant insects disappeared — good supporting evidence, though probably not the only factor.
Other constraints compound it: the exoskeleton must be thicker and heavier as size increases, and moulting becomes progressively more dangerous, since a large soft-bodied animal cannot support itself while its new cuticle hardens.
Aquatic arthropods escape some of this, which is why the largest arthropods alive are crustaceans.