I'm guessing this is all an arranged relationship and possibly even an arranged marriage between these two because of their families.
Takt is probably gay and his family know it and want to keep that a secret from the public as to not shame his father(homosexuality is not very well received in Japan as far as i know), so they forced this relationship to him to keep up appearances.
As for Shizuku, her family probably just wants her to marry him because he is from a wealthy family and her future would be secured financially, that call she received 2 or 3 chapters ago was probably either her mom or dad discussing that.