We get so passionate about the health and appearance of our curls and those of others. But I think there's a fine line between charity and pushiness, and (speaking mostly for myself), sometimes it's easy to cross that line. My mom, for example, who is somewhere in the 4 range (have rarely seen her natural texture to know) has straightened her hair for decades. I've tried to talk her into going natural because in my foggy memory, I loved the way it looked, and am dying to give her all sorts of pretty styles. I even bought a mannequin head to practice on. She's been polite but firm in telling me no. And yet I've kept pushing. She recently said yeah, I can do a natural style on her later this year, but my mom has back-pedaled on this kind of agreement before. So part of this year's resolution is to stop asking her about it and to just accept that she gets to do things to her own hair!
If your brother continues to be averse to your advice, it's probably best to let him do his own thing. It's hair. It's not that serious (except to many of us), unless he's doing something to it that could harm his health (The cancer risk that is the "Brazilian blowout" come to mind, for example ... which he probably isn't doing, I'm guessing).
That said, I agree with the tips above. You could ask if he'll let you give him a basic shampoo. If he agrees, when you take him to the sink you would then of course COwash instead of using shampoo, then just clear it, style it for him and see if he notices the difference, and if he cares about that difference.