How come certain names are crossed out when you decide who to pursue? I am playing through the game currently and after doing V's route I decided to try for Misaki, but I remembered that their name is crossed out. What triggers that?
You have to gain enough favor with someone to romance them -- it's not enough for you to like them, they have to like you too!
Tip: be sure to choose the LI who's route you want to do on the screen where you select who you want to learn more about, and you may be able to get bonus points by choosing roles similar to theirs (for example, if you want Misaki, select the "guns" role in the beginning)!