I think that was just a mistranslation.
It was internally they wanted to promote it as Mhj group but she refused.
My understanding was that Mhj was scouted to debut a new group with bsh. She found a few trainees and started creating the concept and everything.
Bsh wasn't impressed with the concept and eventually just signed Sakura and Chaewon and told Mhj to debut them instead as lsrf, forget about her group and cut the other trainees. It'll be called Mhj's group. She was pissed and eventually negotiated to keep her group as promised that she will get 100% creative freedom. They had a compromise and created a new label for her but it will be 100% owned by Hybe. Eventually with an option to buy 20% at a cheap price.
This was when the relationship between bsh and Mhj soured. Cause mhj refused to help bsh to debut lsrf and bsh didn't like her concept that eventually became more successful that his group.
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I think this is a very good summary of what went down.
It could also be a misunderstanding between them.
Was Bang asking her to drop the NewJeans project and get onboard with the Le Sserafim project, it seem that is what NHJ is implying, there would not have been a NewJeans if she had done what CEO Bang asked.
But I imagine that the Hybe side of the story is that, no, NewJeans would have been a project anyways, just it would have been delayed a bit of time after the debut of LeSserafim.
But as you said, then it became a competition, and when NewJeans broke all kind of records that created tensions, especially with NHJ going out there wanting to take all the credit and downplaying Hybes influence.
Illit was probably created to show her, that Hybe could do the something with out her. and when Illit blew up, then the powers at Hybe were convinced that she was no longer needed, she was also probably pissed and her ego was bruised when Illit did so well with out her.