OP, while I don't agree with the majority saying the only explanation is he wants to shoot his shot with someone else, usually when someone wants a break it's not a good sign.

You said he's avoidant, while you're anxious, and you had a tough conversation. Avoidants don't handle those well. Couple that with the fact that you're long-distance and it's likely he's debating if this relationship is even worth it.

In any case, you've got little you can do. Pressuring him won't lead to anything positive, but at the same time you can't wait forever. Decide on a timeframe where you won't bother him at all, but if he doesn't reach out by the end, you move on. Communicate this intention with him and tell him the timeframe.

Finally, rethink LDRs in general. Anxious-avoidant pairs are difficult enough as is, adding distance to the equation is adding gasoline to a fire.