A third five-year term as party leader would break an unofficial two-term limit that was instituted to try to prevent the excesses of Mao’s one-person rule, notably the tumultuous 1966-76 Cultural Revolution, under which Xi suffered as a youth.
It seems to me that the CCP did not fully grasp that someone with Xi Jingping's background (the ambiguous "suffered as a youth" framing here) would have views of power which do not align with the "party above all else" ethos.