What started ______?
a) you scuba-diving
(b) you to scuba-dive
The answer is (b).
Q1. Why can't (a) be an answer?
Who says (b) is the correct answer? Native speakers would say (a) and NOT (b)
It might be a good idea not calling your child shy in front of other people.
-> It might be a good idea not to call your child shy in front of other people.
Q2. Why should calling be changed to to call ?
It is the form of the sentence you have used.
Say this incident has just happened, and as the grandfather, I say to my daughter:
"Calling your child shy like that in front of other people is not good for the child's confidence."
I am referring to a specific situation that has just happened right then and there.
In your sentence, let's add a few words:
"As a general rule of child rearing, it might be a good idea not to call your child shy in front of other people in future."
Here, I am speaking generally, and suggesting that when situations do occur where the child is shy, at least, don't comment on it to others in front of the child in future.
Student or Learner