How do you discuss two different technical proposals?

I go back to the goal and the constraints. I compare what each proposal gives, what it costs and what could go wrong. If the most important difference is measurable, I suggest a short experiment instead of arguing about preferences.

Not every decision has to be perfect straight away. What matters is whether it's easy to change and how we'll recognise that we need to revisit it. After choosing, I note the reason briefly and support the agreed solution, unless a significant new problem appears. When the question is about your history, you need a real example — the code alone won't tell how the discussion went or who persuaded whom.