Asking/encouraging in my school means “do it”.
No, it doesn't- unless you allow it to. You are a qualified teacher, you can't be told to do anything against your professional judgement of the child's best interest.
(I recently apologised to a child for exactly the same thing. Entirely my idea because I judged that I would only get a very volatile child, new to me, on side by meeting her on her terms. Now I've got a decent relationship with her. Presumably this member of SLT thought they were helping)
That incident has gone now, I wouldn't personally be too bothered by the 'making me apologise' so much as the issue of what's happening to the kids.
If your school is transitioning kids, without parental requests to do so and without informing them, it is your professional duty to whistleblow. Just make sure you know the full situation first, follow the written procedures and the advice of a union Case Officer.
I know that sounds really selfish.
I know exactly how hard things get. You do not sound at all selfish. Look after your own wellbeing and do only what you can- but you can probably do more than you think.