When congress challenged Oklahoma's attempt to move its state capital why did the supreme court sided with the state?

Answer 1

That's not quite what happened.

What happened was more like this: Congress passed an Enabling Act that basically meant that Oklahoma could become a state.

Part of the Enabling Act specified that the capital of the new state was to be at Guthrie, and could not be moved prior to 1913.

Oklahoma moved its state capital to Oklahoma City, about 20 miles south of Guthrie. This upset someone who owned a lot of property in Guthrie, so he sued the state. The "challenge" therefore came from a private individual, not from Congress.

The US Supreme Court found that the provision of the Enabling Act that dictated the location of Oklahoma's capital was unconstitutional, because every other state had the right to determine the location of its own capital, and if Oklahoma could not do the same, then it wasn't being admitted to the Union on an equal basis.

Quoting from the Court's opinion, as written by Justice Lurton:

Has Oklahoma been admitted upon an equal footing with the original states? If she has, she, by virtue of her jurisdictional sovereignty as such a state, may determine for her own people the proper location of the local seat of government. She is not equal in power to them if she cannot.

Answer 2

Congress cannot set political conditions on states.