How does a story being written in first person make a story more believable

Ipronounced his name, offering him at the same time my hand: he took it, smiling and saying, “we shall do very well by-and-by.” then he laid me down, and addressing bessie, charged her to be very careful that i was not disturbed during the night. having given some further directions, and intimates that he should call again the next day, he departed; to my grief: i felt so sheltered and befriended while he sat in the chair near my pillow… (chapter 3) this passage, in which jane first meets the doctor, is an example of