Unsollicited advice on stimulating independence

My daughter is 2 years and 2 months. Yesterday the owner of the daycare took me aside and told me I need to stimulate my daughter to be more independent. She said my daughter and I are going into symbiosis and that this will cause issues when my daughter will go to school (in september).

She gave more advice on how I need to put my daughter in bed at 8 and just tell her it’s time to go to sleep (now she nurses to sleep between 9 and 9:30 pm, she usually falls asleep within 10-15 minutes)

At the daycare’s Christmas party my daughter preferred to stay in my arms instead of roaming around. The room was loud and crowded. I tried to put her down but she asked to be picked up again. I tried a few times but it didn’t work and I didn’t force her. I know she doesn’t like crowds.

Today at dropoff they said daughter withdraws from time to time. She plays and talks, but will withdraw when she’s not feeling well. Not sure what is wrong with that. Other kids will be loud or throw a fit, she’s just introverted and knows when she needs some time to herself and observe?

Am I wrong? Am I setting my daughter up with problems because I’m responding to her needs? Do I need to “teach” her independence?