She is in another relationship / likes another guy.
i can't find on my list a good suggestion so maybe you can read the reviews before watch it. Big (which i hate the ending part) and The Greatest Love.
A Gentleman's Dignity - Has some of what you are talking about and is a must watch. Drama intended for an older audience. Reply 1997 - Also a must watch, with a slightly younger cast.
Pretty much every drama in the beginning is like that...
I'm Sorry I Love You 9 End 2 Outs I Really Really Like You All About Eve Dal Ja's Spring Dr. Champ Hello my Teacher Invincible Lee Pyung Kang Prosecutor Princess Take Care of the Young Lady The Vineyard Man Bad Guy Haeundae Lovers My Fair Lady Que Sera Sera Soulmate Tamra The Island