Porque ele não queria um emprego de secretária.
Picard: 2364 Offered but turned down promotion to admiral as commandant of Starfleet Academy (src: startrek.com)
Uma versão mais detalhada na Memória Alfa:
Mere months upon taking command, Picard was offered a promotion to commandant of Starfleet Academy with the rank of admiral by Admiral Gregory Quinn, but turned it down to retain command of the Enterprise. (TNG: "Coming of Age")
Além disso, ele provavelmente aceitou a sabedoria de um conselho dado por Kirk em ST: Gerações :
Don't let them promote you. Don't let them transfer you. Don't let them do anything that takes you off the bridge of that ship, because while you're there... you can make a difference.