Something inflexible does not bend easily. A stiff back can make you inflexible, or unable to fold over and touch your toes. A really busy schedule can make you inflexible or unable to bend or accommodate your plans for others.
Combine the Latin root words in- meaning "not" and flectere, "to bend" and you have the very meaning of inflexible: not able to bend. Ballet is not for the inflexible or those people who simply are not bendy by nature. Compromise also is not for the inflexible, or those who are really rigid or set in their ways.