The Roosevelt Corollary was an addition to the Monroe Doctrine, a foreign policy statement issued by President James Monroe in 1823 that declared the Western Hemisphere off-limits to further European colonization and any other kind of foreign intervention. The Roosevelt Corollary, issued by President Theodore Roosevelt in 1904, stated that the United States had the right to intervene in the affairs of any Latin American country that was unable to pay its international debts or was otherwise unable to maintain order within its borders.
Roosevelt's decision to support the Panamanian revolt was primarily motivated by the United States' desire to build a canal through Panama. Colombia, which controlled Panama at the time, had refused to grant the United States the necessary rights to build the canal. Roosevelt saw the Panamanian revolt as an opportunity to secure those rights by backing the rebels and helping them to gain independence from Colombia. He believed that the canal was vital to the national interests of the United States and was willing to take whatever steps were necessary to ensure its construction.
Overall, Roosevelt's decision to support the Panamanian revolt can be seen as a reflection of his belief in the United States' right to assert its influence in the Western Hemisphere and to promote its economic and strategic interests in the region.