Also, how did he lose his ability to speak?
Since we never see any direct injury to Chul-min's mouth, tongue, or vocal chords, it is most likely that he knows the heroine will recognize his voice should he speak. Upon realizing her unconditional acceptance, he then speaks the words "I love you"; however, the camera is in a long shot so their faces are not shown during the vocalization so there is speculation that it was a voiceover of his thoughts.
I hope one of the filmmakers can give us an absolute answer to this question.