Disprove that $f(n)=O(g(n)) \Rightarrow g(n)=O(f(n))$?

Question

I know that $f(n)=O(g(n)) \Rightarrow g(n)=O(f(n))$ can be disproved by simply showing a counterexample, such as $n = O(n^2)$ but $n^2 \neq O(n)$? Howeer, for no particular reason(except for my interest), I would like to know how to disprove this conjecture in the general case - like not just by a simple counterexample but using the definitions of big-O. Can you help?