Engaging in sports while infected with mononucleosis is harmful primarily due to the increased risk of severe complications, most notably splenic rupture during the acute phase.
The claim is specific, empirical, and falsifiable. Papers [0], [1], and [7] all explicitly support the claim that athletic participation or physical activity during mononucleosis is discouraged due to the risk of splenic injury and rupture. There are no papers refuting this medical consensus.