Nah, she just doesn't want to come off as incompetent in front of everyone.
It is her firm but Seheon is the biggest breadwinner for the firm and Suhan, a conglomerate, is their biggest client. She doesn't want to lose either of them. But Seheon had warned her before, it was not a good look for a law firm to adhere so much to a single client, no matter how big.
Now Suhan is doing exactly what Seheon had warned her against, they are trying to show them that their firm runs bc of Suhan and bc they did not separate matters with Suhan before it all got ugly, people or rather big clients would have a hard time trusting them.
Seheon would still be fine bc his skills are acknowleged and reknowed in the field but other attorneys at the firm would not get by unscathed. They'll have to drop Suhan bc they can't lose Seheon. Seheon is pure skills and has a lot of credibility and connections. If they drop Seheon, they'll lose a lot more client and business as compared to dropping Suhan. Yes, it'll hurt them financially short term and affect their credibility for a bit, but they can recover of they have Seheon. Also, Seheon is loyal. Yes, he is rigid and come off as callous but he does cares about Mihee and the firm which is why he is willing to guide her the best he can even rn when he is feeling slightly betrayed. He knows she has to worry about the entire firm and not just him.

I wonder if Ms. Song is the one Suhan is having an affair with? She is doing alot knowing for him know Mr. Kang is one of the best attorneys