He needed a dragon to bring down the 700ft high, 300-mile long wall. That's why he patiently waited for the Jon and Co to capture a white walker, the raven to fly out to Dragonstone and then Dany to come in with her dragons.
Maybe because he cannot kill Jon Snow!
Here's my speculation:-
When the long night fell upon Westeros for the first time and the white walkers invaded the western land, the first men searched for children of the forest because they thought that their magic could help defeat the white walkers.
No one truly knows how were the white walkers defeated for the first time, but there are myths that the last hero from the first men fended off attacks from the Wights and finally reached children of the forest to gain their help. The night's watch was formed. The walkers were defeated and they retreated to the far north of Westeros and the Wall was built. Bran the builder (Founder of House Stark), along with the children of the forest were able to cast some spells on the wall to keep the white walkers away. And then the night's watch and the castle black was formed.
According to the legend, the 13th lord commander of the wall (who was stark) fell in love with a white walker (night's queen) and named himself the night's king making that white walker his bride. A marriage was arranged to keep the peace between white walkers and the first men which a tradition in Westeros to keep peace and build alliances. If this is true, then their children will be half white walkers and half stark which explain why the Starks have such an affinity for cold weather and why they tend to be wargs and green-seers. All the Stark children are wargs, they each have a special connection with their respective direwolves. This half white/half stark also explains to some extent why Melisandre was able to bring Jon back to life.
Jon, having ancestry from both Targaryen (Fire) and Stark (Ice) makes him the perfect candidate for the song of Fire & Ice and bringing peace to Westeros.