I just google "the races of man"; none of you are even close to right. Here's the correct listing:
"The races of man; elf, human, dwarf and halfling"
I don't doubt your word that you found that in Googling. However, since it clearly refers to Tolkien's world, one must use Tolkien's classification.
Elves are not man Dwarves are not man Humans, of course, are. And to my knowledge Tolkien did not clearly show what relationship Hobbits have to man, if any. He does refer to them as "people", or "one of the free peoples".