I am male, 62, no children and "the baby" of three siblings. My brother, 8 years older and first born, was as you described your youngest brother when he and his wife raised their two boys. I was at the emergency C-section in Africa the day it rained 7 inches and it took a long bumpy ride to the hospital floating through flooded intersections in the night and her several hours of fruitless labor. Because she had a long recovery from surgery, I personally cared for the first born for more than a month while my brother did his medical mission to eradicate smallpox and inoculate for measles.
In my experience, which included 20 years listening to my mother lament my brother's over-the-top care and protection of his children, tells me that it was not a function of birth order but one of a very strong desire to be right, self-guiding and a perfect parent. When children grow into adulthood, there is often an obsession with going your own way and proving to everyone (who have always tried to sway your thinking and convince you of the errors of your ways) that you have it right for you and yours (so leave me the **** alone).
You are an adult woman, but not more of an adult than your brother. You simply have more experience, and your own personal experience at that. Your are a degreed teacher, but you don't bother to spell check. As a teacher, you must also know that one's own experience is the real teacher in life. As a teacher, you can only influence, cajole, love, badger, suggest, etc. You cannot actually do for someone that which they must do for themselves, or they won't learn. (Give them a fish or teach them to fish? Life is in the verbs.) You want to tell and show your brother how you are right and he is wrong, and he has suffered this syndrome for years simply by being last born. As adults, learning is the responsibility of the learner. Teachers can only help the willing learn.
Let it go. Stop being an expert mother, teacher, big sister or whatever your wagging, nagging finger makes your younger brother feel like. Learn to ask leading questions, such as, in a loving, caring and curious way, "What else does your book say?" and "How did your body build its immune system?" When he has his next child, he will soften and relax anyway; all parents grow tired and less vigorous in raising subsequent children. But for this first child, he will grow up knowing he must be first, be responsible, and take the advice (always) of his parents until that day he can break away from the family yolk and oppressive, cloying influence and do it his own way too. Life is a cycle, and hopefully an upward one. That's why the Frank Sinatra song hits home with so many people: "I did it my way."