Online hate speech has become increasingly prevalent on social media, causing harm to individuals and society. While automated content moderation has received considerable attention, user-driven counterspeech remains a less explored yet promising approach. However, many people face difficulties in crafting effective responses. We introduce CounterQuill, a human-AI collaborative system that helps everyday users with writing empathetic counterspeech - not by generating automatic replies, but by educating them through reflection and response. CounterQuill follows a three-stage workflow grounded in computational thinking: (1) a learning session to build understanding of hate speech and counterspeech, (2) a brainstorming session to identify harmful patterns and ideate counterspeech ideas, and (3) a co-writing session that helps users refine their counter responses while preserving personal voice. Through a user study (N = 20), we found that CounterQuill helped participants develop the skills to brainstorm and draft counterspeech with confidence and control throughout the process. Our findings highlight how AI systems can scaffold complex communication tasks through structured, human-centered workflows that educate users on how to recognize, reflect on, and respond to online hate speech.