According to the Supreme Court's summary [0], the CDC was arguing it derived its authority primarily from US Code 42 section 264(a) [1] > The Surgeon General,

According to the Supreme Court's summary [0], the CDC was arguing it derived its authority primarily from US Code 42 section 264(a) [1] > The Surgeon General, with the approval of the Secretary, is authorized to make and enforce such regulations as in his judgment are necessary to prevent the introduction, transmission, or spread of communicable diseases from foreign countries into the States or possessions, or from one State or possession into any other State or possession. For purposes of carrying out and enforcing such regulations, the Surgeon General may provide for such inspection, fumigation, disinfection, sanitation, pest extermination, destruction of animals or articles found to be so infected or contaminated as to be sources of dangerous infection to human beings, and other measures, as in his judgment may be necessary. There is also 42 CFR 70.2 [2] > Whenever the Director of the Centers for Disease Control and Prevention determines that the measures taken by health authorities of any State or possession (including political subdivisions thereof) are insufficient to prevent the spread of any of the communicable diseases from such State or possession to any other State or possession, he/she may take such measures to prevent such spread of the diseases as he/she deems reasonably necessary, including inspection, fumigation, disinfection, sanitation, pest extermination, and destruction of animals or articles believed to be sources of infection. The main legal arguement is weather the second sentence of 264(a) should be read as expanding or restricting the authority granted by the first one. Even without that question, it is not clear that the first sentence on its own should be interpreted so broadly as to allow an eviction moratorium. It is also weird to say that no one challanged it. It has been a controversial action from the start. And has been succesfully challenged in the courts. [0] https://www.supremecourt.gov/opinions/20pdf/21a23_ap6c.pdf https://www.supremecourt.gov/opinions/20pdf/21a23_ap6c.pdf [1] https://www.law.cornell.edu/uscode/text/42/264 https://www.law.cornell.edu/uscode/text/42/264 [2] https://www.law.cornell.edu/cfr/text/42/70.2 https://www.law.cornell.edu/cfr/text/42/70.2