In order to answer this and to craft your argument, you should start by thinking about what sorts of things we have to get licenses in order to do. You should then compare parenting to those things and show how they are similar.
Let us think of some things for which we must get licenses. We must get licenses to drive. We must get licenses in order to be a teacher. We must get a license in order to practice medicine or law.
Now, let us think about why it is that licenses are needed for these things. First of all, they are all hard to do. If something is easy, there is no need to have a license to prove that you know how to do it. Second, all of these are things that would cause problems if they are done improperly. If someone does not know how to drive or does not know anything about medicine, they can kill people if they try to do those things. The results will not be as dire if they try to teach or practice law, but they will still be bad. Thus, it would seem that we can conclude that people should get licenses for activities that are difficult to do properly and which, if done wrong, could harm others.
So now you need to prove that parenting fits these two criteria. Is parenting hard? Absolutely. Parenting requires self-control. It requires the ability to put others before oneself. It requires the ability to say no to your kids when they really want things. It requires you to be able to keep your temper in check when it is very hard to do so. Parenting well is not an easy thing. Does bad parenting hurt people? Absolutely. Bad parents can harm their children physically by beating them or (and this is much less bad) by letting them sit around all day eating junk food and getting no exercise. Bad parents can harm their children for the future by failing to help them learn so they can do well in school or by failing to teach them things like self-control.
By going through these steps, you should be able to persuade your audience. List things that require licenses. Discuss the factors that make it so that licenses are needed for those things. Show that parenting has those characteristics as well. This will logically prove that a license should be required for those wishing to have a child.