Influenza is still a frequent seasonal infection of the upper respiratory tract, which may have deadly consequences, especially for the elderly. This is in spite of the availability of vaccines suggested for persons above 65 years of age. Two types of conventional influenza vaccines are currently licensed for use—live attenuated and inactivated vaccines. Depending on local regulatory requirements, live attenuated vaccines are produced by the reverse genetics technique or by classical reassortment in embryonated chicken eggs. Sometimes, the efficiency of classical reassortment is complicated by certain properties of the wild-type parent virus. Cases of low efficacy of vaccines have been noted, which, among other reasons, may be associated with suboptimal properties of the wild-type parent virus that are not considered when recommendations for influenza vaccine composition are made. Unfortunately, knowledge surrounding the roles of properties of the circulating influenza virus and its impact on the efficacy of the reassortment process, vaccination efficiency, the infectivity of the vaccine candidates, etc., is now scattered in different publications. This review summarizes the main features of the influenza virus that may dramatically affect different aspects of the preparation of egg-derived live attenuated vaccine candidates and their effectiveness. The author expresses her personal view, which may not coincide with the opinion of other experts in the field of influenza vaccines.