He's online but doesn't read my messages. Why?

The green dot shows an app status, not where someone's attention is. It cannot establish that he saw your message, chose another person, or decided to ignore you. Your actual conversation gives you more to work with than the dot does.

If you need a response, the useful question is when he can talk. Muting activity indicators can also take the repeated checking out of your evening; it need not be a move designed to make him notice your absence.