Simply because abandoning territorial claims will do nothing: It will neither eliminate the military threat of the "North" Korea, nor would it relax the tensions.
It requires enormous amounts of legal work, including adopting amendments to the Constitution of Korea.
This is why: Both governments claimed sovereignty over the whole Korea, however in a different manner: Constitution of Korea (Article 3) claims its sovereignty over entire Korean peninsula ; Constitution of "North" Korea (Article 1) claims its sovereignty over all Korean people .
Article 2 talks about "the liberation of the homeland" (obviously, including the "Southern" Koreans) from "imperialist aggressors".
There is no peace treaty signed yet (the 1953 Agreement deals with armistice only );
Retracting the territorial claims can be done on a mutual basis , probably as a part of Peace Treaty , when both sides to retract their claims; There are reasons to think that the DPRK is not going to keep its promise, should any be given.
Most likely, adopting amendments to the cornerstone articles of the Constitution would require conducting a National referendum and convincing the majority of the citizens.
We could safely assume that there is a powerful lobby against that: the Wikipedia article for Korean reunification contains some introductory links that indicate controversy in public opinion.
politics.stackexchange.com/users/2984/bytebuster for Long Usernames
As a German the message By now it's completely obvious that the Korean peninsula won't be reuniting any time soon.
has no merit for me at all .
I can assure you as contemporary witness that nobody expected a German reunification as far as 1988, two years before the final reunification.
It was a big stroke of luck that Russia had no interest to aid the old government with military help (yes, they asked frantically for it) and that the resentment was running so deep that the own army denied any involvement and
the demonstrations were so big that neither police nor Stasi could suppress it anymore.
Neither is the argument of the different enormous economic differences convincing .
Yes, the reunification of Germany was extremely costly and long, but it also showed opportunities.
The land will split into the two regions and the enormous inner demand and a good supply of cheap workers could boost the economy.
During the 90s many countries were thinking that Germany tried to bite off more than it could chew and was a sinking star (Remember the "old Europe" quip from Rumsfeld 2003?).
Well, the situation now...there is an idiom in Germany.
It is translated as "Pity is given as a present, but envy must be earned".
We really don't know what the future will bring.
If the North Koreans continue to annoy and disgrace China, their presumed ally or if a revolution is triggered in China or if the government in North Korea are simply not able anymore to support their population and their soldiers(!)...
I do not rule out that South Korea will be reunited during my lifetime.
politics.stackexchange.com/users/5644/Thorsten S.
It is the official government policy of both North Korea and South Korea to unify.
This is due to the historical fact that Korea was unified before World War II.
Both countries were unified for more than a thousand of years , under various names, including the Greater Korean Empire from 1897 to 1910, Joseon from 1392 to 1897 and Goryeo from 918 to 1392.
Both countries have a shared history and culture.
In addition, they have also proclaimed reunification as an eventual goal after the Korean War, signing the 7 · 4 South and North Korea Joint Statement , outlining this aim.
However, given the recent development of North Korea's nuclear weapon programme, it has made denuclearisation of the Korean peninsula a bigger priority than reunification.
While reunification may be increasingly difficult now due to the divergence of their economies and social structures, it's worth remembering that they have only been separated for less than a century, as opposed to being unified for a millennium.
As such, both North and South Korea will not give up their claims of each other.
politics.stackexchange.com/users/9638/Panda
Why doesn't South Korea give up its claim on North Korea?
Let me ask a rhetorical question.
Why doesn't the north give up its claims on the south?
By now it's completely obvious that the Korean peninsula won't be reuniting any time soon.
No it isn't.
Obviously Germany split around the same time as the Koreas but still reunified.
If there is any angst about that, I haven't heard it.
Beyond the question of whether or not the community wants to reunite, there is also the constant possibility of military action.
The United States is not going to rule North Korea under martial law.
If the United States goes to war with North Korea, the only practical end (assuming a US victory) is for South Korea to take over in the North.
And if South Korea does that, their own constitution would require that they allow the north's citizens to vote.
They'd be reunited.
Personally, I would expect them to reunite by the end of the century.
Obviously North Korea's model is not sustainable.
If it was, they wouldn't have to sell chemical weapons to Syria just to keep the lights on.
The Koreas will either find a way to work together, which will inevitably to reunification, or North Korea will collapse, which will inevitably lead to reunification.
The only path to keeping the two separate that I can see would be for China to manage North Korea as a client nation.
And China doesn't seem very interested in doing that.
I suppose Russia could take the place of China if they wanted, but I'm not sure that anyone wants that either.
politics.stackexchange.com/users/4666/Brythan
One must also keep in mind that this situation is not two groups of people who are in conflict.
It is largely the Kim dynasty in the north promoting the divide, not the people of N Korea.
Only the Kims and a few cronies benefit from the current situation.
Should the Kim dynasty fall, as in something unpleasant happening to Kim Jong Un, reunification becomes a possibility, albeit one with considerable economic issues in revitalizing the destitute north, and political issues with China.
N Korea acts as a buffer between the capitalist south and China.
politics.stackexchange.com/users/14788/tj1000
By now it's completely obvious that the Korean peninsula won't be reuniting any time soon. It's also quite likely that the South wouldn't want a full reunification anyway given the enormous economic differences between the two countries.   So why won't South Korea officially abandon their claim to the North of the peninsula? What benefit is there in maintaining the charade?
Why doesn't South Korea give up its claim on North Korea?
politics.stackexchange.com
<north-korea><south-korea>
politics.stackexchange.com/questions/26897
politics.stackexchange.com/users/7434/JonathanReez
Abandoning territorial claims will do nothing: It will neither eliminate the military threat of North Korea, nor would it relax the tensions.  It requires enormous amounts of legal work, including adopting amendments to the Constitution of Korea because both governments claimed sovereignty over the whole of Korea in a different manner. The Constitution of Korea  (Article 3) claims its sovereignty over  entire Korean peninsula;  The Constitution of North Korea  (Article 1) claims its sovereignty over  all Korean people. Abandoning their claim will not change the current climate of tensions and a National Referendum would also be required. Furthermore, both North and South Korea wish to remain unified. 
Abandoning their claim will not change the current climate of tensions and a National Referendum would also be required. It is also government policy of both North and South Korea to unify. 