Neo cannot be sent as fractions because they are not a currency like Bitcoin. They are "Shares," as in Shares of the company Neo. That is why their name used to be Antshares and Neo gas was called Antcoins. By owning Neo you actually own a small fraction of the Neo company and that is also why Neo pays you a dividend (Neogas) when you own Neo-shares. You get part of the reward because you are part owner. You could think of them as being similar to buying shares in the stock market and those shares paying you dividends. So the Neocoins (Gas) can be divided but the shares cannot.
The reason you can buy fractions of Neo on an exchange is a bit more complicated.