In the elementary steps of a reaction, why do we assume that the coefficients of a reactant correspond to its order? Recently, I was taught that the coefficients of the reactants in an elementary step of a reaction indicates that reactant's order. Why is this the case? I thought that the order of a reactant was not related to its coefficient.

For example, in the following termolecular reaction mechanism

$$\ce{A + 2B -&gt; C + 2D}$$

the rate law is $k[\ce{A}][\ce{B}]^2$. Why is this the case?

EDIT: Also, for equilibrium reactions, do we always assume the coefficients of the reactants to provide the order for those reactants? What about for equilibrium reactions involving multiple steps?
If a reaction has just one step, it's named an elementary reaction. In this reaction all of reactant directly participate on reaction and effectively collide with each other. So, the order of reaction corresponds to its coefficient, but if a reaction is not a elementary reaction, there isn't any reason for colliding all reactants with each other. For example, consider the following overall reaction:

$$\ce{A + B + D -&gt; F}$$

Assume the corresponding mechanism is constituted of two elementary reactions:

$$\ce{A + B -&gt; C}$$
$$\ce{C + D -&gt; F}$$

As shown above, there is no need to collide A with D or A with C ... Then, in these type of reactions coefficients are not corresponded to order of reaction .