Where does 1.3606 approximation ratio come from for vertex cover approximation?
The fact that nobody found a $1.99$ approximation doesn't necessarily mean that the problem of finding one is $\mathsf{NP}$-hard (e.g., it might be the case that that $\mathsf{P} \neq \mathsf{NP}$ and a polynomial-time $1.99$-approximation algorithm exists, we are just unaware of it).
Additionally, we can prove that finding a $1.3606$-approximation is a $\mathsf{NP}$-hard problem, i.e., if $\mathsf{P} \neq \mathsf{NP}$ no $1.3606$-approximation algorithm exists. This is not a direct consequence of the previous fact, but a separate result by Irit Dinur and Samuel Safra. The details can be found here.