There exists a very close and well-known relation between a vertex cover and an independent set in a graph $G(V,E)$ (): if $S$ is an independent set of $G$, then the set $V$ \ $S$ is a vertex cover of $G$. The same complementarity relation holds obviously for a maximum independent set $S$ and the set $C = V$ \ $S$ that is a minimum vertex cover of $G$.
MY question is: Both max independent set (MIS) and min vertex cover (MVC) are NP-hard and they have complementarity relation. Why MIS cannot be approximated to a constant factor in polynomial time (unless P = NP) , while MVC is approximable within approximation ratio 2?
C. Berge. Graphs and hypergraphs. North Holland, Amsterdam, 1973. https://en.wikipedia.org/wiki/Independent_set_(graph_theory)#Approximation_algorithms