All children, (and adults) have their own... intrinsic and inherent personality and dispositions.
Sure, the parents raise the child. But along with that, a child has their own developmental based... phases as well. Which needs to be considered. If not, there will be... LOTS of frustration in the parents and then upon the child... if the "expectations" on the child is not congruent with a child's developmental based, cognition etc.
At this age, emotions... are not even, fully developed.
The human brain, is not even fully developed until 26 years old.
At this age, a child does not even have, "coping skills" or communication skills... nor do they even have complete understanding of "emotions" nor the exact names for their emotions.. they do not have hindsight or the ability for full deductive or inductive reasoning etc. Nor of abstract concepts socially or emotionally.
MOST young 3 years old... have apprehensions socially and this is normal. It is not "wrong" or them being bratty.
BOTH my kids at that age... were shier. It was them. I knew that about them. I did not make them, be "extroverts" if they were not. I nurtured, who THEY were and are. Because of that... they trust themselves, and have remarkable intuitive ability... to gauge social situations, the intent of others, and how to CHOOSE friends... wisely.
My kids are now 6 and 9... they are not longer the "shy" or apprehensive 3 years olds they used to be. But now, they are, astute about their "radar" for other people and situations.
That is golden.
I am proud of them.
We taught them, from 2 years old, the names for feelings, about social scenarios, how to "analyze" their feelings about things, and how to choose friends and how to communicate etc.
It was not about "manners" or about pleasing others, for my sake.
It was about, teaching our kids to KNOW themselves, and to TRUST themselves and to be themselves for who they are. They are thus, not "followers" and are, well mannered wise children. For their ages and per social situations.
I never got "embarrassed' about my children, if they were "shy" or hesitant at social gatherings, nor was I apologetic to others about their shyness, nor did I try to make my children more extroverted, even if they were shy.
We just nurtured our kids, as they were, in disposition. And thus, they are very self-assured children who can, speak up or gauge social cues, very well. And they can manage themselves, per their cues.
My daughter especially, though shy when younger, she has an astute "radar" about others... and is often correct, in DISCERNING, situations. Socially.
MANY kids, who are 2,3,4,5 years old... can be, more introverted. We cannot mold... a child's every tendency. But instead, teach them how to manage in a way that is developmentally and age appropriate, per their age stage.
I never... "taught" my kids to be friendly to others, if they did not want to.
Why? Because, I wanted them to learn to TRUST themselves and their own intuition about situations. A young kid, does not put on "airs." They are not even social experts yet, nor socially astute. Some adults aren't even experts at it. A 3 year old, is just developmentally, 3 years old.
Expectations, needs to be age appropriate.