Students struggle to put down their ideas in the limited time given. Students can find writing under a time limit particularly stressful, and may feel like they cannot produce thoughtful responses in the time given.
Share questions or prompts ahead of time. You can give students time to think about their answers (thus easing the stress of time limits) by emailing out questions and prompts ahead of section. You might even just share the questions/prompts at the start of section and move on to something else before you have students begin writing, naturally leaving time in section for students to start thinking about their responses.
Emphasize the preliminary nature of their responses. Make clear to students that, while they should provide reasons for their responses, they aren’t expected to have a fully-developed argument right from the start. In fact, part of the purpose of the discussion afterward is to encourage students to clarify, revise, and perhaps even outright switch their thinking based on the feedback of their peers.
I don’t have time in section to properly facilitate a discussion of every student’s response. Section time is finite, and you may struggle to find time to discuss every student’s unique response. However, simply letting student contributions go unrecognized and unused is not especially conducive to an inclusive discussion.
Group similar responses together. Look over the written responses before convening the discussion. Organize the discussion around the question/prompt students respond to, as well as patterns in those responses. So, for example, if you asked a question about the classic trolley dilemma, you might ask one student in favor of diverting the trolley to go first and explain her reasoning, and then invite those who agree to elaborate upon the answer (without repeating it). You can then invite those who disagree to offer their criticisms.
Break into smaller groups. If you provide multiple different questions/prompts, you might consider breaking your down by question/prompt responded to and holding multiple mini-discussions in parallel.
Keep a record of unaddressed student contributions. Either in class (on the board, in your notes, etc.) or through an online document, maintain a list of responses, questions, and objections that don’t get properly addressed in class discussion. This not only recognizes otherwise ignored student contributions but can also be used as fodder for future sections discussion or even as inspiration students can use for writing and other assignments.