Because YT chose to insert themselves in front of the DMCA. When someone copyright claims your video, they're not actually sending a DMCA, they're doing a YT-s

Because YT chose to insert themselves in front of the DMCA. When someone copyright claims your video, they're not actually sending a DMCA, they're doing a YT-specific process that just happens to look sorta like the DMCA notice/counternotice process without involving the legal system.