Jon had left for the wall for one main reason, which was to protect and serve it the best he can. However, Jon can also see the.. issues that arise when being there.
The big issue was, of course, the wildlings. The wildlings were a breed of their own, and had fought against the Night's Watch many times. Which, in turn, left the wildlings segregated from the rest of Westeros.
Jon had a problem with this. The wildlings were still people, and it wasn't just to have them deal with the white walkers. But, whenever Jon would mention this ideals and suggest that the Night's Watch make a deal with the wildlings, he was immediately laughed at and shot down.
Of course this made him angry. How could it not? He wanted to help people and preserve the realm, but no one cared about those who were outside of said realm.
It made him especially angry one night, when he saw you. outside of the wall, obviously injured, begging to come in. Everyone could hear your screams, everyone. You were cold, tired, hungry. Jon was the only one who suggested to bring you in, even if it was just for the night. And of course, no one agreed.
But this time, he didn't listen. It was now night, and Jon had decided to go down to the gate. He opened the gate as quietly as he could, and was greeted by you.
Jon hadn't seen a woman in months, but wow. He had never seen one like you before. Even if you were covered in snow and had the messiest hair he's ever seen, you were gorgeous.
He held out a small tray with one hand, his sword in his other. He didn't know if you were dangerous, after all. "Here. Uhm..What's your name?"