For those of you, who may not have noticed this before: houses are no living beings; there is no need for respiration. What then is meant by breathable walls? There is some confusion. Are we talking about air exchange? If we do, I can only fiercely recommend making the building envelope as airtight as possible (see Airtightness for details on that).
However, in case this is about water vapour: let it pass! I do not recommend trying to tighten your construction to disable the transport of water vapour. Why is that? Have a realty check: no construction will ever be entirely vapour tight. We are not manufacturing Swiss watches, we are building houses, which is – however organised you may be – a lot messier than watchmaking. A millimetre gap in an interior vapour barrier however is enough to let water vapour enter the construction cavity. Inside a cavity, it will diffuse. Then what? If the vapour meets a cold surface, it will likely condense. This likelihood is increased when a vapour barrier is fitted on the outside of the construction. There is no way out for the vapour then, and it is unlikely that the vapour finds its way back to the original 1 mm gap - after all it is not playing paperchase, and not working against the pressure gradient either.
In a colder, continental climate, water vapour resistance should decline from the inside to the outside of building components. This is because in winter, water vapour pressure from the inside of a heated home is a lot higher than from the outside. So some resistance for the passage of vapour within the inner layer is good, to prevent “overloading” the construction with vapour. The remainder of water vapour that passes the inner resistance layer can then escape through a low resistance layer to the outside. It is always better though, to not set the internal resistance too high (like you would with a a vapour inpermeable material like polyethylene), because this prevents drying of the construction in summer (when water vapour pressure is likely to be higher on the outside).
In a subtropical climate, a balance has to be struck, for there might not be a prevailing pressure tendency from one direction. WUFI is the right programme to determine needed water vapour resistance in this case. A free version is available for not-for-profit use.
Occupants of buildings however might well be living, breathing things; fresh air should be provided to them, preferably in a controllable manner (see why under Ventilation). Air should be fit for human consumption. Therefore I shudder when I see ventilation systems that draw in the “fresh” air from unused roof spaces. For all I know, on my ceiling floor there may be thick layers of dust, ants, mould and dead rats. I certainly would not store any food up there; it is a space completely outside my routine scrutiny. And please think thoroughly about the pre-warming effect: usually, when your roof is so warm that you can utilise the warm air – it may already be too hot to do this comfortably. There may be some hours in winter, when the roof actually collects desired warmth. However, if you are not home during the day (and unfortunately the sun in winter only shines during business hours…), you will not hugely benefit from this. And there are those winter nights, too, when the roof is actually colder than the surrounding outside air temperature, and that is when you need warmth the most.