I have to see the full sentence and "까다" has the meaning of criticizing. I'm not sure whether it would appear in the dictionary since it is informal. I think it derived from the meaning "kick". I think it means someone who criticizes someone else.

The meaning depends on the context. 까는 is modifier form of 까다 or 깔다. There are many meanings of 까다 or 깔다 For examples, 바나나 껍질을 까는 사람 means "the person who peels a banana" 목소리를 까는 사람 means ""the person who lowers voice" XX(someone)를 까는 사람 means "the person who reproaches someone" etc.

I am a bit confused as to the verb you used. I think you might've used 까다롭다 instead because 까다 means to hatch. When '는' was added to it, it kind of means 'that/who ____'. Seeing how 까다롭다 means to be picky or stubborn, I think the sentence you are saying is MEANT to mean 'the person who is picky'.