Antonyms for the word "most intransigent" would be words with opposite meanings such as flexible, adaptable, compromising, cooperative, amenable, or reasonable. These words describe someone who is willing to listen, negotiate and make concessions to reach a resolution. In contrast, someone who is described as "most intransigent" is marked by refusal to change one's views or to agree about something. It is important to note that being intransigent can sometimes be necessary, especially when standing up for what is right, but being able to compromise and see other perspectives is an equally important quality in many situations.