Concept:
The oxidizing power of halogens decreases down the group:
\[\begin{aligned}
F_2 \gt Cl_2 \gt Br_2 \gt I_2
\end{aligned}\]
A more reactive halogen can displace a less reactive halide ion from its salt solution, but the reverse is not possible.
Step 1: Analyze the displacement order of halogens.
\[
\begin{aligned}
F_2 &:\quad \text{Highest oxidizing power} \\
Cl_2 &:\quad \text{High oxidizing power} \\
Br_2 &:\quad \text{Moderate oxidizing power} \\
I_2 &:\quad \text{Lowest oxidizing power}
\end{aligned}
\]
Step 2: Check each reaction.
\[
\begin{aligned}
(A) &:\; F_2 \text{ oxidizes water to oxygen} && (\text{Yes}) \\
(B) &:\; Cl_2 \text{ cannot oxidize } F^- \text{ to } F_2 && (\text{No}) \\
(C) &:\; Cl_2 \text{ displaces bromine from bromide} && (\text{Yes}) \\
(D) &:\; Br_2 \text{ displaces iodine from iodide} && (\text{Yes})
\end{aligned}
\]
Step 3: Identify the reaction that does not occur.
Since chlorine is less reactive than fluorine,
\[\begin{aligned}
Cl_2 \;\text{cannot oxidize}\; F^-
\end{aligned}\]
Therefore,
\[\begin{aligned}
\boxed{2KF(aq)+Cl_2(g)\rightarrow 2KCl(aq)+F_2(g)}
\end{aligned}\]
does not occur.
Hence, option \(\mathbf{(B)}\) is correct.