appeal to possibility?

At best, there's at least one missing premise.  Without it, there's no link between the potential for children to improve things and your plan to have children.  I suspect the missing linking premise(s) would be something like "I want to make the world a better place." and "I will take action make the world better".

While appeal to possibility could be seen to apply (it is possible – but not guaranteed – that children make the world better), I've always understood this fallacy as relating more to situations where the assumed outcome is actually quite unlikely to the point of being improbable – perhaps related to "anything is possible".  

Adding quantifiers might help understand my point:

• All children always do make the world a better place.


• Some children always do make the world better


• Some children sometimes make the world better.


• It's theoretically possible, but not very likely, that children make the world better.

Each of those statements can be seen as an equivalent version of "Children can ...", but each would lead to a different conclusion.  I think that the conclusion doesn't follow from the premise, making non sequitur a better description of the fallacy.

The implied argument would be:

P1: Children can make the world a better place.

P2: You want the world to be a better place.

C: Therefore, you should try to have children.

Yes, this is a fallacious conclusion. Assuming P1 and P2 are true, the conclusion is not necessarily true because P1 allows for the possibility that children can not make the world a better place.