
I didn't praise someone on my team and NOW she is threatening to leave...
Seeing a lot of negativity here. Let me set the record straight.
A few months ago, we were in the middle of a critical project, the kind where deadlines were harsh. My team had been putting in long hours, and there was no doubt they were doing good work. We were on track to meet our goals, and honestly, it was impressive how everyone pulled together. But something happened during a meeting that left me with a tough decision to make.
One of our team members, had just wrapped up integration at the client side. He’d been leading a portion of the project, and his work was good. After his presentation, people expected that I will praise him.
But I didn’t.
It’s not because I didn’t think she did a great job. She absolutely did. But I knew that in this moment, giving her too much credit or over-hyping her contribution, could throw off the balance. You see, the entire team had been working hard. She may have been leading that piece, but it was the collective effort that made it successful. If I praised her, it could make the others feel like their work was less valuable.
I’ve seen it happen before. You give one person too much recognition, and suddenly, the dynamic shifts. People start noticing. They wonder why their work didn’t get the same level of acknowledgment. It sows the seeds of competition, and it messes with the team dynamics.
So instead of compliments, I did what I always do. I acknowledged the work briefly, thanked her for her presentation, and moved on. Now, she is threatening to resign. What should I do? Am I wrong?

Everyone has a different opinion
Yes, you should appreciate her in front of everyone so she will vet motivate and contribute more.
Similarly you should appreciate others who worked together.
If she did extraordinary things then others are also aware. So no one feels bad.

So you have mentioned "People expected that i will praise him/her"
Then in the next paragraph
"if i praised him/her, it could make others feel like their work was less valuable"
Not coherent to me

You could have appreciated the efforts of the entire team and her efficient leadership and appreciated how they all worked together and made it possible. Never not too late to do it.

Irony is when ur entire team hv informed her that it was good job and u didn't recognise... Once my manger told me just ok in the meeting for the best work I did... Everyone told me he intentionally didn't recognise you, it's very difficult to make a career under him just leave the place or change project.

Let her go even you tell her you can release her early if she wants may be she is just bluffing or may be it’s just a start later she will come with something else , but connect with your team and praise the team so that the team knows you value them and there is no place for threats