homotopy groups of a pair and quotient It is known that if $(X,A)$ is a good pair, for example a $CW$ pair,
then $H_k(X,A)\simeq H_k(X/A)$ for every $k$.
Is it true for homotopy groups of $CW$ pairs? If not, what is the counter-example?

No it is false . $\pi_k(D^2,S^1)=0$ for $k\geq 3$ ( follows from long exact sequence of Homotopy pairs). But $\pi_k(D^2/S^1)=\pi_k(S^2)$ which is non-zero for infinitely many $k$.
But there is a partial result which says , if a CW pair $(X,A)$ is $r-$connected and $A$ is $s-$connected, with $r,s\geq 0$, then the map $\pi_i(X,A)\to \pi_i(X/A)$ induced by quotient map $X\to X/A$ is an isomorphism for $i\leq r+s$ and a surjection for $i=r+s+1$.
