Why? How?
because he just left with no explanation
But he was afraid. They never told each other how they felt about each other, so he probably assumed he was just another customer for Nagi and nothing else. Also, it was because of work so it was inevitable.
But if you think about it, the Kazuki never stopped thinking about Nagi, and for 5 years his eyes still wandered rooms to try and find him. He also kept the ring for all those years, and this time he wanted to be in an official relationship with him.
I understand that it was a wrong move on not telling him where and why he was going, but as I said, he was afraid of how he would’ve reacted.
DAMN this was great but i still hate the seme