Obviously Sugawara doesn't also like Izumi.
I believe she was surprised by Kazusa's new found confidence and resolve; something that, despite her mature demeanor and good looks, she hasn't achieved yet. The fact that she had to lie to the theater director that Izumi was her boyfriend just to show him, was testament to her immaturity.
The director was (and may still be) her first "love", and that is hard to get over, especially when it's not resolved. Yet, all I said is but a mere simplification of what actually went on in her mind. There's something about having your first love with someone unreachable and unavailable (the director) that changes people. Do differentiate this kind of affection from idolatry, as those 2 are not the same and have different effects. It can make people develop a fear of intimacy and romance. Easily resolvable through therapy.