All electrical wire and connection components create resistance to the flow of electricity. This resistance causes electrical energy to be converted into heat energy. As example of the process, this is how the filament in incandescent lightbulbs produce light -- resistance in the filament causes it to heat up to the point where it glows (i.e., incandesces.).
There is a relationship between resistance and the amount of electrical current, described by Ohm's Law. (The Ohm's law formula includes circuit voltage but we can ignore that because we're dealing, at this point, exclusively with nominal 12VDC circuits.) In turn, based on the physics, there is an indirect relationship between wire size and resistance.
In a nutshell, smaller wire and higher current (amps) means more resistance. Conversely, larger wire and lower current means less resistance. At a certain point, moving from small to large and high to low, the resistance drops to point where it's negligible. (And the resistance curve effectively "flat-lines.")
So, electrical circuits are designed to use wire at least large enough to carry the expected current. In practice, slightly larger wire is preferred, with economic factors being the sole determination of how much larger is too large.
In addition to wire, connection components (wire terminals, screws, nuts, bolts, and so on) also create resistance within a circuit. Loose/corroded/dirty/etc circuit connections greatly increase the amount of resistance in a circuit. In response, more amps in the circuit are required to meet the demands of the circuit's load. This is exactly where well designed circuit usually go into overload conditions. (Even if this does not lead to catastrophic overload, problems with faulty circuit connections waste electricity, converting much of it to heat rather than actually powering the circuit's load.)
CPDs prevent catastrophe by serving as the "weak link" that fails before the rest of the circuit.
So, while wire should be sized for more that the expected current in the circuit, CPDs should be sized to match or, at most, slightly exceed the expected current.
The CPD's amperage rating should never exceed that of the wire and connection components. (Otherwise, the wire and devices become the circuit fuse.)
(Reliable companies that manufacture CPDs practice stringent quality control because of the legal liabilities involved in a CPD failing to perform as designed and rated.)
