This was because the wife of Imperial Prince Tamehira was MINAMOTO no Takaakira, who had the title of Sadaijin (Minister of the Left), and the FUJIWARA clan was afraid of the Daigo-Genji (Minamoto clan) becoming a maternal relative to the emperor.
これは為平親王の妃が左大臣源高明だったためで、醍醐源氏が外戚となることを藤原氏が恐れたためだった。