Why does the supreme court have its own building?

because it is one of the 3 branches of the government.

After the federal government was established in Washington D. C, the court was placed in the United States Capitol, in a small place in the basement. As the senate expanded and progressively occupied more spaces, the court had to move from one room to another within the capitol on two occasions: first in 1810, to the chamber that left the senate, a space that had to share "with other courts, like the Circuit Court of the United States, and the Orphans Court of the district of Columbia". And again in 1860, when It moved to the today called "Old senate chamber", where it remained until its current location.

The supreme court remained in the capitol until 1935, except for the period 1812-1817, during which it temporarily left the city of Washington D. C, as a result of the Anglo-american war of 1812. In 1929, the presiding judge, William Howard Taft, got a proper building for the court, with the purpose of distancing itself from congress, as an independent branch of the government, which began to occupy in 1935.