Q:

Why must the forward reaction and the backward reaction follow the same pathway? 

It is often claimed that a (normal) catalyst catalyzes the forward and the backward reaction to the same extent, so the equilibrium position is not shifted. 
I would like to ask why must the forward reaction and the backward reaction follow the same pathway? 
I could imagine a mechanism for this reversible reaction from $A$ to $D$:
$$\ce{A <=> D}$$
$$\ce{A -> B<=> D}$$
$$\ce{A <=> C <- D}$$
So that the forward reaction and the backward reaction must follow different pathways, as one step of both pathways are irreversible. 
Is this scenario impossible in reality?  If so, why?  If not, is there any example in real life? 

A:

A catalyst cannot change the equillibrium of a two component reaction, because that'd always violate the principle of conservation of energy. 
Also there is no such thing as an irreversible reaction.  If the backward reaction is very unfavourable energy-wise, the catalyst won't change that, but you cannot have two highly exothermic reactions in your funny circle anyway.  Where should the energy come from?