I don't think there's anything insidious or unreasonable in asking someone to prove their identity to vote.
You would like to create an additional check on voting that will prevent some legally entitled voters from voting. This, I believe, is undeniable.
All I'm asking for you to do is provide a rational, objective, empirical justification for doing it. Not emotionally how you feel about it, but facts. Why do you believe undertaking this action is necessary, what objective are you attempting to accomplish, and why is preventing some legal voters from voting is a worthwhile price to pay to achieve this objective? Again, factual evidence.
I don't think those are unreasonable questions to ask.