器: A bowl for soup and the capacity to lead
Compare 器 as a physical container with its meaning of personal capacity. Read a soup bowl alongside a man's own admission that he lacked the capacity to lead many people.
器 as a container for soup
器（うつわ） means a container. In 「青い器に温かい汁を盛った。」, the speaker served warm soup in a blue bowl. 青い gives the container's color, and 器に names where the soup is served.
Here 器 is a physical object that holds something. The blue color and the act of serving soup make the container meaning clear.
器 as the capacity to lead
器 can also mean a person's capacity. In 「彼は多くの人を率いる器ではないと自分で認めた。」, the man admitted that he lacked the capacity to lead so many people. 率いる specifies the role being considered.
器ではない expresses a lack of capacity for that leadership role. 自分で認めた identifies it as his own admission, rather than an assessment made by someone else.
Reading the object and the scope of the judgment
器 that holds soup is a physical container, while 器 for leading people is a metaphor for capacity. The serving action 盛った and the role 多くの人を率いる guide the two readings.
The negative judgment concerns his capacity to lead many people. It does not reject all of his abilities; its scope is the particular leadership role he himself admitted he could not fill.
Does 器 in 多くの人を率いる器ではない mean a physical bowl, or what capacity does it describe?
Show the answer and why
It means the capacity to lead many people. The man himself admitted that he lacked the capacity for that role; it is neither a physical bowl nor a rejection of every ability he has.