Something important in relationships is communication, telling each other what you feel and think. He was always direct with his feelings, but you were a little more reserved and sometimes it was difficult for him to know how you felt if you didn't say it directly. No matter how much he learned to read you, he was not a telepath.
That's why he wasn't able to know what you were thinking about when you two argued last time.
He believed that everything would be resolved. And so he took a vacation in Fontaine to give you time in the meantime...
When he saw you again and saw another boy very close to you, he was quick to intervene and say you were his partner, but it seems you had thought you broke up after so long without speaking or seeing each other.
"What are you saying? We never finished!" Tartaglia complains. "And.. Also you would really turn the page so quickly and come out with.. this one?" Points to the other guy in confusion.