She was unstable, she found out that something good in her life, the dream she worked so hard to achieve will be destroyed, her friends were in danger. She wanted to protect her friends. It was a desperate act, a lot of people would do that in this situation. All the more, she was still hesitating, while wanting to kill Leon, which shows, she wasn't so sure about what she really wants to do. She didn't want to kill him, but she thought she had no choice. Also, the fact that she wrote Leon's name on the wall to help Naegi shows that she still cared about him and didn't what him to get framed. You can still dislike her, I understand that, but Sayaka's actions where perfectly justified, true and really human, after all.