Why in this dialog is「ございません」the appropriate answer?

「兄弟がありますか。」「いいえ。私は兄弟が（＿＿＿）。

I understand that ございません would parallel あります in the first sentence, but
shouldn't I use the polite form of iru to describe the non-existence of living
things?
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2019-11-21T02:25:57.183
73166
2019-11-21T02:25:57.183
36074
question
keigo
Use of ございます to describe existence