Okaaayy half of the things in that chapter probably made no sense so I'm going to explain.

Y/Ns mothers quirk is that she can fly (she has wings)

Y/Ns dad's quirk is a mix from two others (an Arranged marriage is the cause) he has inhuman speed and foresight.

Y/Ns mother is abusive to her family and sees her daughter as a toy. When she discovers her quirk she sees this as an opportunity for Y/N to be 'useful' and plans an Arranged Quirk marriage with her daughter and an infamous villains son (Atio).

(Every generation of the L/N family had an arranged marriage,and she's trying to carry it on)

Her dads quirk is foresight and he saw What was going to happen so
he told Atio to pack a suitcase with necessities and told him the plan, they later went to get Y/N.

Basically the dad saved them from the arranged marriage and sent them to England where they would be safe and in doing so got himself killed.

(He arranged for someone in England to take them to the safe house. )

Your quirk is
Flight
Foresight (you can predict the next half hour or so)
Speed (gOTTa Go FaST)

You can fly (you have wings but they were cut by your mother)

You have inhuman speed and foresight for a half hour which makes you pretty op . 😤

(both your parents are pronounced dead)