Option C: 'And' connects words, phrases and clauses.
It is relevant to the given sentence, as here it connects the nouns 'people' and 'animals'. The function of 'and' is addition, and that's what is performs here. It adds two nouns 'people' and 'animals' that perform the same function 'breathe out'.
Hence option C is correct.
Option A: 'Are' is a verb that means 'to exist'. It does not add proper meaning to the sentence. (People are animals breathe out)
Option B: 'Either' expresses a choice between two. The given sentence does not indicate any choice.
Option D: 'Were' is the past tense of 'are'. Similar to 'are', it does not complete the sentence in meaning.
Hence options A, B and D are incorrect.