Parenting Tactics: "Stay Listening" vs. Coerce or Force

I’m reading this parenting book that is making me question a lot about what we do with our kids/ see as ‘normal’...

For instance, my kids started up swim lessons again today. And both started crying the second we got to their lane (even though they were prepped and ready and excited beforehand).

Traditional method (ie what the swim coaches wanted to do and what I did before this book): take crying child away from parent quickly, so as to ‘rip the bandaid’ if you will, and even restrain the child forcing them to stay even though they clearly want to leave/ be with the parent. 
The child may calm down after 5mins, or 20mins, and go along with the lesson. And this is seen as a success. Proof that the kid could tough it out.

New method: parent stays with child as long as necessary, letting child cry. Parent doesn’t make any attempt to force the child to go in; no bribes, no big pep talks, no shaming (“see, all the other kids are doing it” or “I paid a lot of money for this lesson so you have to get in”). 
Parent just listens. And restates the desire for the child to join the class, but if met with more tears, continues to just listen and offer comfort to child. 

The child may cry the whole lesson. But more often than not, the child ends up leaving the parent’s arms, on their own, and joins the lesson. If not day one, then day 2 🙂

This book made me realize that I have no idea what is causing the tears - and most likely my kids can’t verbalize it in this moment either - their logical mind has been hijacked by some strong emotion, so I either let them feel it and be sad (& get glares from other adults thinking I’m torturing my kid and ‘just making it worse’), or I see the crying as natural response to a kid going through a strong emotion, and let them cry til it’s out of their system.

I’m leaning towards the new method; I realized if I was in my kid’s position - being forced into doing something I didn’t want to do - sure, I might suck it up and go along so I don’t make a fool of myself, but if anyone literally pulled me into something that I felt was unsafe or scary, I would punch them! 
So why is it ok to pull a kid away?

And even though it might appear that they got over it, did they really? And what did we just teach them? You should submit to someone bigger than you to make other people happy, and push your own feelings down?

I know this could ignite a bit of a rough discussion, but I figured it was one worth having 🙂 esp since I don’t know what is right, all I know is what felt more right to me in the moment today...

This is the book by the way: "Listen: Five Simple Tools to Meet Your Everyday Parenting Challenges"