I think this sentence has a typo: "Now we have a Seek Predicate on DateAdded and a Predicate filter on DelFlag with a much-improved query cost (and less logical reads)." -- looks like "DelFalg" should be "Gender" instead
I think this shows why indexes should lead with the equality columns, then inequality columns. I used to be in that camp; order the index columns by selectivity. Now I avoid date fields for leading columns of indexes even if they're very selective.
I would rephrase your first sentence to ..."why indexes should lead with equality columns and then range searches." Inequality columns (from your query) will almost always cause a scan rather than a seek.