Nakatta vs inakatta

[Siesta]

ケーキを食べたのは、私 ＿＿＿＿＿＿＿＿＿＿
（ I was not the one who ate the cake.) (Negative-past, Polite)
Why is the answer ja arimasen deshita and not ja inakatta?

I did not even question this when I first learned in, but I thought iru is to be used for living things and aru for inanimate objects.

[Sidgr]

This is like saying:

It is not I that ate the cake.

The verb is in this sentence doesn’t concern your animacy so that distinction is not relevant.

[Siesta]

Thank you! I was just thinking about this and realized that, and I was about to delete this post.