Have the writers or anyone associated with TNG ever commented on why they chose to make Picard uncomfortable with children?
As @Hypnosifl points out P. 23 of "writer's bible" by Gene Roddenberry does state that Picard has a certain dislike of children.
However I believe that paragraph sums up why Picard dislikes children rather well. It states (and the memory alpha page on the Stargazer corroborates) that Picard was in command of the Stargazer for 22 years. During this time Picard commanded a ship with no families or children at all. When he was posted to the Enterprise he was apprehensive about serving on a ship with children and other civilians. He wasn't sure how to respond to them because he was used to the more regimented crew of the Stargazer.
In fact the writer's bible goes on to state:
Captain Picard has his share of idiosyncrasies, one being the fact he is not yet fully comfortable with having families and children aboard a vessel he commands. ... Picard supports its concept cautiously, while having his own private misgivings. He has not had much experience dealing with children...
Picard was just used to having only Starfleet Officers to deal with on his ship and didn't know how to respond to passengers.