Let $f(n)=o(g(n))$. By definition there exists $n_0$ so that for all $n>n_0$ it holds that $\varepsilon \cdot g(n) \geq f(n)$ for $\varepsilon>0$ however small.
So, in plain language, starting from a certain point, $g(n)$ grows significantly faster than $f(n)$. However, how about the part before asymptotic behaviour kicks in, when $f(n)$ and $g(n)$ can go wild?
Is it possible that for some $x\in[0..n_0]$, $f(x)=M$ gets a maximal value so that $g(n) < M$ (for all $n$)?