What exactly are you referring to when you say "sensitive"? I have what I would call a more sensitive boy. He is 11 yrs in 6th grade. He has a July birthday and will be 12 over this summer.
My son doesn't cry and never has been a "crier". But he is sensitive to others' feelings and is very quick to apologize and want to make someone else feel better if he sees they are upset (usually his younger sister, lol). He is quick to get his feelings hurt if he feels like he has disappointed you in some way. And quick to become angry with himself if he feels like he has made a mistake of some kind. I would never have thought of him as a leader... always more of a follower... but in a good way: He respects authority and doesn't get into trouble, generally speaking. And he wants everyone to be included in games and is quick to befriend other kids. He will accede his wishes if it means that someone else gets to play too. He does have a lot of creative ideas though, and while I have never seen him insist on playing "his" game... the "group" often ends up doing some version of his ideas... So maybe he leads in a more suggestive way, rather than forceful... which is a good skill to have, imho.
So if that is the kind of thing you mean by 'sensitive', then, yes, my son is. I worried a little about him at the beginning of this year, starting middle school. He seemed so much smaller than the 7th and 8th graders I saw at the school. But then I saw him with his friends (and this was his first year in public school, so it was ALL new for him, including his friends) and all his friends are smaller like him. They just haven't hit their growth spurt yet. Although, he has recently pudged out in the waist (a FIRST for him) and has some aches behind the knees that seem to indicate imminent growth! So next year.. he will be one of those "big" 7th graders. :)
My son has been doing Tang Soo Do since he was 5 yrs old, and has had mentor/friendships with older boys through church families since he was about 3 yrs old. He acquits himself very well with ALL ages, including adults.
I think it depends on what your son is exposed to and comfortable with. My son has always been almost the youngest kid in his class. But I happen to think that the quality of the kids in the class has a lot to do with how that affects the kids. His karate class has a huge range of ages in it, and my son has almost always been one of the youngest. He is a higher rank than many teens, because he started so young, and he "helps" them with their skills in class sometimes. All the instructors (some are late 50's, some are as young as 21) are wonderful role models and mentors to ALL the students. And they don't shy away from teaching the younger kids to have respect for themselves along with other people. They teach the students how to show respect, while simultaneously showing respect to their students (listening without interrupting, looking them in the face/eye when speaking, "yes ma'am" "yes sir", along with the respect that accompanies martial arts in particular - higher rank is in the front row in class, bow to instructor when handing them items, thank target holders, bowing to flags upon entering the classroom, etc.)
Sorry to go off on a tangent about karate. But it has been such a blessing in reinforcing the values we instill in our kids. And it is a huge confidence builder as well. Not just the physical aspect, but the mental/emotional confidence as well. They do compete with each other (through sparring), but the goals are to improve yourself... not to be better than someone else. There's no "I can't do this as good as so and so"... the focus is on doing it better than YOU did before.
If you are not comfortable starting your son this year.. then by all means do what you feel is right. That is all we as parents CAN do. But don't base your whole decision off of the story of another parent and HER child. Her child is not yours, and you should be cautious about projecting her misgivings onto your son. Just as I have no regrets about starting my son "on time", my son is not your son. Only you know what is best for him.
Good luck with this momentous decision.