The answer lies on the Korean peninsula itself, and specifically in North Korea, which is engaged in a nuclear weapons drive and has boasted in the past of its ability to turn Seoul "into a sea of fire."
Through the dispatch of troops to Iraq, Seoul hopes to disarm that threat by winning over the United States to its policy of engagement with North Korea.
"The main line of thinking among policy makers (in dispatching troops) is that it would not be helpful in terms of South Korea's national interest to ruffle Washington's feathers," said Park Kie-Duck of the private Sejong Institute think tank.
"It would be difficult for Seoul to push through with its policy of reconciliation towards North Korea should Washington put brakes on it."
There is a sense that many in power harbour profound misgivings about the US-led occupation of Iraq even though a contingent of 600 troops is already based in the Middle Eastern country.
South Korean leaders who have championed the dispatch of 3,000 extra troops starting in August have done so without apparent enthusiasm for the Iraq campaign itself and the deployment has been delayed for months.
The beheading of South Korean Kim Sun-Il by Islamic militants this week has sharpened a divide within the country over a war that has never been popular here and in which Koreans can see no link to national interests.
World leaders praised President Roh Moo-Hyun for moral fortitude in refusing to concede to the militants' demand to scrap plans for the larger deployment.
The liberal reformer's steadfast support for the troop dispatch at the request of Washington could cost him politically as support among his younger, more progressive backers, wavers.
But Roh has carefully framed the deployment as a way of promoting the achievement of an unrelated goal -- a necessary evil contributing towards a greater good.
Though Roh has said the troop dispatch is for relief and rehabilitation work only, not for combat duty, the moral argument used by the United States that sending troops to Iraq is a noble gesture to free an oppressed people from tyranny is not part of public discourse here.
For Roh, support for the United States in Iraq is a pragmatic step that he hopes will help resolve once and for all the biggest strategic threat facing the country -- the North Korean nuclear standoff.
Specifically South Korea wants Washington to ease its hard line towards the Stalinist state by offering concessions that could lead to a negotiated settlement and avoid bloodshed or the collapse of North Korea.
For those young South Koreans who swept Roh to the presidency in late 2002, America's hard line represents a greater threat to security than the communist North Koreans.
Many younger South Koreans who burned US flags in demonstrations 18 months ago are angry with Roh for supporting Washington. They would like him to cut the alliance and drop the troop dispatch.
This and similar anti-US thinking stirred Seoul National University professor Kim Seong-Kon to anger.
"Dear ungrateful, unabashed young people of Korea, how could you tear off the national flag of an ally that has been helping you secure freedom, national defense and economic prosperity, for the past three scores (of years)?" he asked in a commentary.