WASHINGTON — Petty Officer 1st Class Kate O’Toole’s naval career hopes were dashed when the chief selection list came out last month, and her name was not on it.

“I just don’t get it,” O’Toole said. “I look great on paper: I aced the chief’s exam, I’ve deployed four times, I had letters of recommendation from two admirals, and I won the Marine Corps Marathon last year. Now what am I supposed to do?”