Trelawney may have said the prophecy, but Voldemort is the one who created it. He is the one who gave it meaning and life. If he discarded it as just nonsense, Harry would have grew up normally, like any other kid in the Wizarding world. Instead, Voldie killed his parents, got himself killed in the process and afterwards made killing Harry his prime mission. He weaponized Harry by accidentally making him a Horcrux and making him susceptible to using a Phoenix wand, just like himself.

He outright refuses to let his Death Eaters kill him. There was no magical binding, or vow, or pact that forced him to duel Harry. He only wanted to do it himself because of some random woman's words that one of his servants heard over a decade ago. His own naivety was the only thing that gave any substance and relevance to the Prophecy. Not the prophecy itself. 

The man literally cornered himself into unwanted suicide.  