You cant.

Sending countless messages is desperate no matter which way you spin it, you are desperate for a response. Same with clingy, you're clinging onto the idea of your relationship/friendship.

So in short the clingy desperation already shines through brightly.

How about you type whatever it is you feel compelled to say to him in a memo or word doc. That way its out of your system without actually sending it to him.
I do that when my bf is in his mancave, I harass my memo instead of him

He's not responding and only he knows why, I suggest you leave him alone because you'll drive yourself and him nuts with forcing the issue. You can't make him explain himself and you cant make him want you either.

Maybe he'll want to reach out and explain once you stop contacting him. Maybe it seems like a "hot topic" and he wants to avoid starting a fire, so he may be waiting for you to cool off and calm down. If that's the case, the more you text, the longer his silence drags on.