Sentential logic can't see any structure inside atomic statements. What makes this significant for logic is that some arguments composed entirely of atomic sentences, from the standpoint of sentential logic, are still clearly valid. This is obviously valid. And this is, equally obviously, an invalid sequent. The problem is simply that our system of sentential logic can only catch part of the story of validity.
Some arguments are valid because of the way they are structured with sentential connectives.
Sentential logic explains why these are valid. Other arguments, such as our last example, are not valid for that reason, but they are nevertheless valid. Predicate logic is an extension of sentential logic which studies why those additional arguments are valid. In fact, different atomic sentences can share some of those smaller parts. The words 'John', 'Mary', 'likes', 'hates', 'mangoes', 'manatees' appear in different places in these various examples.