No we don't..I am the mom to 5 Boys! I was taken back by this response, seriously. Now, none of my kids began sports at age 3, it is not offered in our small town, begins at age 4, for tball only and it used to be age 5, until last year they changed it. All of mine, have chores, even my 3 yr old. They all pick up after themselves. The older ones do much more. But the younger 2, pick up their dinner plates, keep their room clean, make their beds to the best of their ability and put their folded laundry away. They will even sweep and mop, or try too.
Is he still a toddler yes. Can he write his name yes, read simple letters, yes, count yes, write numbers, yes. Is he still a toddler yes. Can he dress himself, yes, put shoes on, button and zip his coats, yes. But is he still a toddler yes.
Is he a baby no, is he "the baby" yes. Does he ask to be carried, sometimes, sometimes he will stand at the top of the stairs and ask and won't budge. He is not jealous of anyone younger, since he is the youngest. It is just him testing how far I will go. Do I give in, depends on what I am doing.
I enjoy every minute of him wanting me to hug, kiss, carry him. Time goes by so fast. I now look at "my first born baby" who is now 14 and a freshmen in highschool and think, wow, that went by so fast.
I don't agree with giving in, to just give in, I don't agree with throwing tantrums. Each parent handles them differently and in their own way. If you feel strongly about not carrying him at a specific moment in time, then don't and stick to your guns. If you want to give in, then go, give in. He is not a 10 yr old asking to be carried.