I asked a girl out for dinner, but she didn't reply by texting. She replied that she couldn't go tonight because she had something to do. What is the reason?

Her performance either shows that she doesn't want to go, or that your relationship is not close enough for her to cancel the evening date.

Invite girls to dinner in person, it is better to send text messages. If you ask her face to face, she will think that you are more serious and pay more attention to this date. Girls will be more likely to ask for a date when they see your sincerity.