Many women are divided when it comes to this subject. They really do not know whether to be the first to text or wait until they are texted. However, there are valid reasons to text him first. One important thing to take into account is that men are very patient and slow and that some men can give their numbers to women even if they are not interested.
If he is the one who offered his number, a day goes, days and then weeks, and you see no text from him then he is probably not interested. Nevertheless, you must understand there are some guys who are generally shy but is not for you to use shyness as excuse to be the first to text him. In this case, you can start the conversation using other valid reasons.
Another reason to text him first is that some men love it. It somehow boosts their ego to have a woman they are interested in text them first. You have to be careful though not to appear desperate or needy. After you establish the conversation, he will be happy to be the first to text next time. There is no reason to lose your potential happiness just by being afraid to text first.
Finally showing your interest could be the reason to text him first. In most societies, the culture is that men should be the first to make the initial advance. However, this does not hold waters anymore. If you are interested then you must let him know about it. Maybe this will make him realize his own feelings for you. These reasons should address your question- should I text him first?