Yet all men are not drawn, are they? Many remain stubbornly apathetic or hostile. You have to qualify the "all" somehow, so you will make it mean "all who believe." That is true, except that men are drawn first and believe afterwards as God opens their hearts (Acts 16:14).John 6:44 makes it very clear that God must draw a person to Him and Jesus makes it very clear in John 12:32 who that is: "And I, if I be lifted up from the earth, will draw all men unto me."
I believe that the "all" in John 6:44 means "all manner of people"- male and female, rich and poor, slave and free, Jew and Gentile and so forth (cf. Galatians 3:28). Take a verse like Philippians 4:13. 'I can do all things through Christ who strengthens me.' What does the "all" mean there? Does it mean every single thing in the world? Can Paul do brain surgery or walk on the ceiling? Of course not! It means that through Christ, Paul can do all manner of things: specifically, to be abased and to abound; to be full and to be hungry; to abound and to suffer need (v.12); in fact, all the things God requires him to do..