The use of algorithmic decision making systems in domains which impact the financial, social, and political well-being of people has created a demand for these decision making systems to be ``fair'' under some accepted notion of equity. This demand has in turn inspired a large body of work focused on the development of fair learning algorithms which are then used in lieu of their conventional counterparts. Most analysis of such fair algorithms proceeds from the assumption that the people affected by the algorithmic decisions are represented as immutable feature vectors. However, strategic agents may possess both the ability and the incentive to manipulate this observed feature vector in order to attain a more favorable outcome. We explore the impact that strategic agent behavior could have on fair classifiers and derive conditions under which this behavior leads to fair classifiers becoming less fair than their conventional counterparts under the same measure of fairness that the fair classifier takes into account. These conditions are related to the the way in which the fair classifier remedies unfairness on the original unmanipulated data: fair classifiers which remedy unfairness by becoming more selective than their conventional counterparts are the ones that become less fair than their counterparts when agents are strategic. We further demonstrate that both the increased selectiveness of the fair classifier, and consequently the loss of fairness, arises when performing fair learning on domains in which the advantaged group is overrepresented in the region near (and on the beneficial side of) the decision boundary of conventional classifiers. Finally, we observe experimentally, using several datasets and learning methods, that this \emph{fairness reversal} is common, and that our theoretical characterization of the fairness reversal conditions indeed holds in most such cases.