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The bichloride ion $\ce{HCl2^-}$ does exist, but it requires other environment than usual solutions in water. E.g. solution of $\ce{[N(CH3)4]Cl}$ salt and undissociated $\ce{HCl(solv)}$ in nitrobenzene solvent, as mentioned in the ACS link of the Oscar's answer. It is the scenario that kind of does not leave any more favorable choice for chloride ions.

For water solutions scenario, the key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$

The bichloride ion $\ce{HCl2^-}$ does exist, but it requires other environment than usual solutions in water. E.g. solution of $\ce{[N(CH3)4]Cl}$ salt and undissociated $\ce{HCl(solv)}$ in nitrobenzene solvent, as mentioned in the ACS link of the Oscar's answer. It is the scenario that makes the partial hydrogen charge in $\ce{H^{(+)}-Cl{(-)}}$ quite favourable for chloride anions.

For water solutions scenario, the key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$

The bichloride ion $\ce{HCl2^-}$ does exist, but it requires other environment than usual solutions in water. E.g. solution of $\ce{[N(CH3)4]Cl}$ salt and undissociated $\ce{HCl(solv)}$ in nitrobenzene solvent, as mentioned in the ACS link of the Oscar's answer.

For water solutions scenario, the key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$

The bichloride ion $\ce{HCl2^-}$ does exist, but it requires other environment than usual solutions in water. E.g. solution of $\ce{[N(CH3)4]Cl}$ salt and undissociated $\ce{HCl(solv)}$ in nitrobenzene solvent, as mentioned in the ACS link of the Oscar's answer. It is the scenario that kind of does not leave any more favorable choice for chloride ions.

For water solutions scenario, the key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$

The key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$

The bichloride ion $\ce{HCl2^-}$ does exist, but it requires other environment than usual solutions in water. E.g. solution of $\ce{[N(CH3)4]Cl}$ salt and undissociated $\ce{HCl(solv)}$ in nitrobenzene solvent, as mentioned in the ACS link of the Oscar's answer.

For water solutions scenario, the key is the presence of undissociated $\ce{HF}$ and the ability of $\ce{F-}$ to make hydrogen bond with $\ce{HF}$. Neither is available for $\ce{HCl}$ and $\ce{Cl-}$. There are just very minor traces of undissociated $\ce{HCl}$ in water and $\ce{Cl-}$ would not have bound to it even if it had been there.

There are no $\ce{HCl}$ or $\ce{KCl}$ in water as molecules. There are hydrated ions $\ce{H+(aq)},$ $\ce{K+(aq)}$ and $\ce{Cl-(aq)}.$ Hydrated molecules $\ce{HF(aq)}$ are there in hydrofluoric acid or in acidified fluoride solutions, reacting:

$$\ce{F-(aq) + HF(aq) <=> HF2^-(aq)}\tag{R1}$$

Hydrofluoric acid is weak mainly because of forming the stable ionic pair, so ion $\ce{H3O+(aq)}$ is mostly not free:

$$\ce{HF(aq) + H2O(l) <=> H3\overset{+}{O}\bond{...}F-(aq) <=> H3O+(aq) + F-(aq)}\tag{R2}$$

The structure of $\ce{HF2-}$ is $\ce{[F\bond{...}H-F]-}.$ There is also $\ce{[H-F\bond{...}H]+}$ in concentrated hydrofluoric acid or liquid hydrogen fluoride:

$$\ce{3 HF <=> H2F+ + HF2^-}\tag{R3}$$

Liquid hydrogen fluoride has such a high boiling point due $\ce{HF}$ chain linked by hydrogen bonds:

$$\ce{[\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}H-F\bond{...}]}$$