What does it mean for girls to send text messages to boys on their own initiative? What kind of psychology is it?

This shows that she is still alone, a little lonely, and still has a good impression on you!

Even if I don't want to confirm that I am boyfriend and girlfriend with you right away, I am willing to communicate with each other, care about each other and keep in touch!

As for chasing or not, it depends on whether you are willing or not!

For love, sometimes everything is an obstacle! Sometimes, what age, distance, family background,,, is not a problem! It depends on how the parties operate!