Let's have some flashback about S04E04,
When a white walker brings one of Craster's son to Night King. So, the scene goes like this,
[WikiPedia] Later, a White Walker retrieves Craster's son. The Walker travels to the White Walkers' fortress in the Lands of Always Winter and lays the child on an altar made of ice. The leader of the White Walkers, the Night King, approaches and places his hand on the boy, transforming him into a White Walker.
So, they've shown that the Night King can convert living into white walkers by just touching them.
But in S08E03, it didn't seem to be the case when Arya approached the Night King to kill him.
The question is, How is Arya not transformed into a White Walker when the Night King grabs her by the neck?