Why would the CIA not admit to interviewing Oswald in June of 1962?

The CIA may not have admitted to interviewing Lee Harvey Oswald in June 1962 due to concerns about operational security and confidentiality regarding intelligence methods and sources. Additionally, acknowledging the interview could have raised questions about the agency's oversight of Oswald, especially after his later involvement in the assassination of President Kennedy. Keeping such information classified might have been viewed as necessary to protect the integrity of ongoing investigations and the agency's reputation.