Q.it is the 1st of June and My Rose of Sharon does not a leaf, but the branches do not snap when I bend them. What is my problem
why does my Rose of Sharon not have any leaves yet at the 1st of June. The branches seem to be supple?

Plants that are in full sun will leaf out earlier than those in partially sunny areas. But no matter where it is planted, one of rose of Sharon's other disadvantages is that it is susceptible to winter injury and twig die-back.
That is not to say that your "unleafy" branches are dead and won't come back; as you noted, they are still flexible. So it is indeed possible that they are even later than the rest of their siblings.
If the plant does not leaf out with more patience, try pruning it down to stress the roots into growing. It you have no new growth, the plant may have been lost.