Why is this the answer?

The answer is nose because this is a super clever riddle that uses playful word pictures to describe one of the most important parts of your face. It is a puzzle that makes you think about an action, like running, but the answer is actually an object that is part of you! Let us look at the first clue: "I can run but not walk." When you hear the word "run," you probably picture a race at school or a puppy zooming across the yard. But there is a special, secret way that your nose can "run." Think about when you have a cold, or when you step outside into the chilly winter air and your nose starts dripping a little. You might hear an adult say, "My nose is running today." This does not mean your nose grew legs and is walking away! It simply means that liquid is flowing out because you are sneezing or have the sniffles. This is the fun trick the riddle is playing by using the word "run" in a very different way. Now for the second part of the riddle: "Wherever I go, thought follows close behind." This is even easier to solve when you think about it! Where does your nose go? It goes everywhere you go, because it is stuck right in the middle of your face. And where do your thoughts happen? Your thoughts, memories, and clever ideas all come from your brain, which is safe inside your head, just behind your nose. Since your nose is always on your face, and your brain is always in your head, the two of them are always together. Your clever thoughts are following close behind your nose everywhere you go. Your nose is a silly, wonderful part of you that can "run" without walking, and is always followed by your very best thoughts.