As a Demon Slayer, he must focus on his job and his duty. So he has no choice but to break up with you, he's afraid that you'll get hurt if you stay close to him. The Flame Hashira is miserable, he can't forget about you even though he tried. He still love you so much, there no doubt about it anymore.

Rengoku now is determined..

He must take you back, using his charm. He'll do anything to get you love him and stay with him again..

Anything..