Why does my dad think i dont love him?

Well we have gotten into arguments dealing with how i act. He thinks that i don't love him because he doesn't see it. When a disagreement comes up he brings up an incident when i was five and went to visit my grandma, my mom and dad picked me up from the airport and i was mad because i got sick with my grandma and couldnt go to an event that i wanted to go to. So my parents thought that i didn't miss them. Like as if all this time i don't love him. What can i do to show him i do?