Do boys care that girls don't take the initiative to send him text messages?

He cares about proving that he has a good impression on you, likes you and wants to develop with you. If you also have a good impression on him and like him, take the initiative to send him. After all, falling in love is not a person's business. On the contrary, if you are not interested in him, you should make it clear to him that it is not good for one of them to delay his feelings.