Suppose we're working over an algebraically closed field $k$. If $V\subseteq\mathbb{A}^n$ and $W\subseteq\mathbb{A}^m$ are affine algebraic sets, there is a well known bijective correspondence
$$
\operatorname{Mor}\_\mathrm{reg}(V,W)\leftrightarrow\operatorname{Hom}\_{k-\mathrm{alg}}(k[W],k[V]).
$$

I assume this fails in general if $V$ and $W$ are not affine algebraic sets. Consider the case where $V=\{\*\}$ is a point, and $W=\mathbb{A}^2\setminus\{(0,0)\}$. So $V$ is affine, but it's also a well known fact that $W$ is not affine. My question is, why does the natural map

$$
\operatorname{Mor}\_{\mathrm{reg}}(V,W)\to\operatorname{Hom}\_{k-\mathrm{alg}}(k[W],k[V])
$$

fail to be surjective, so that the bijection does not hold in this case?