what과 that 중 어떤 게 맞나요?

“For his final scouting project, he made a speech to his fellow high school students, telling [that/what] it was like to be treated as a disabled person.”에서 what은 되고 that은 안 되는 이유가 궁금해요.
telling 이하 문장이 불완전한지도 알려주세요.