There's something fundamentally weird about LinkedHashSet, isn't there?
You use it when you want to have a guaranteed order of iteration (insertion order or LRU order). Except, what would happen if you took your LinkedHashSet and, say, stored it into a HashSet? Later you'd be iterating through the elements of this greater set, and "your" LinkedHashSet will be there, but it might have a completely different iteration order! It might even suddenly be an LRU-ordered set while your original one was insertion-ordered. You'll have no idea what to expect.
So you wanted the iteration order to be respected, and you thought LHS would give you that. But it wasn't respected; it was just discarded.
So... a little bit strange. Just a little.