Alice wanted to stick to her plan, act useless, and participate as little as she could in the sports event.
But she miscalculated. She thought that she would go scot-free if she annoyed Philip with her awful use of weapons, and she would be allowed to sit back in the benches, but it was the opposite.
Because Philip already knew that she was a girl capable of many 'things' he felt it was an insult that she was putting up such a crappy show to try and sit back.
And if that was what she wanted, he would not give her what she wanted.
Even Clarissa felt insulted by her actions. She felt she was looking down on her and acting weak just to give her leverage but someone as prideful as Clarissa would not sit back for that.
She was determined to defeat Alice in a fair fight and not through flimsy tricks. After all, she was that confident in her bow and arrow skills.