Are they splitting the coin up into smaller wallets so they do not keep all their eggs in one basket? Any other reasons why?
Maybe they move it because they pay like online or maybe they move some into there wallet to protect there bitcoin. They keep it safe as you said air maybe they don't want to put an eggs in one basket. Many people are holding big amount of bitcoin so they want to keep safe there bitcoin.
Hmmm...I can't imagine how you thinking from these word. These word is indeed often to use to give a suggestion to everyone in order to they don't choose one place investment to store their money. So, they just store their money to one place only and it is bitcoin. But the purpose of these word (idiom) is you have to choose another place to store your money such as in ETH or LTC. So, to pair up this idiom with what whales action as OP said it is not suitble. And maybe you have to know, the safest way to store bitcoin it is not in an exchange, you will have many risk that will you face. But hardware wallet is the best place as far as I know.