There are a few parts to it as has been mentioned in other posts.
First the capital city will usually be a center of political power in the country. In that way if it’s captured then a lot of that can be disrupted. I’m practice what that means is that changes in the overall direction of the war (such as planning to recapture the capital) may not be communicated or communicated as efficiently, knowledge feeding into those decisions may not be able to get to the right people as efficiently. Plus there is going to be confusion about who is actually in charge for a while as there will be a possibility that people at the top of the chains of command have been captured.
Second the capital city will likely be a major concentration of administrative power. Similar to political power above this means that there can be a major disruption of the flow of information that’s required for fighting the war. The political direction can be solid and unified, but if the information in what is needed and where it’s needed can’t be transmitted efficiently then that makes things much more difficult. This goes both ways as it would be reasonable for some military units to “go dark” rather than reporting their position and status as normal and potentially sending that information to the enemy.
Third is that the capital city is also going to be a concentration of economic power. That will make it more difficult to fight the war as it means that buying necessary supplies, paying troops and the workers supporting them becomes more problematic with the enemy in control of the banks. That goes double for international transactions.
The final problem is morale. If the enemy has taken the capital city then it will seem to a lot of people like they’ve effectively won. That will cause a lot of military operations to be less efficient because of the morale loss ( who’s going to fight harder, a soldier who believes that they can stop the enemy winning, or a soldier who believes the enemy has already won)
There are ways to mitigate each of these problems, and modern technology can help a lot in that regard too. None of them separately or together guarantee that if you take an enemy’s capital city that you’ll then win, but the enemy will have to do things pretty spectacularly in order to win after that
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