Context, context, context...
The context of Jesus' statement about none coming to Him apart from being drawn by the Father was in relation to those who would be His disciples, not the general populace of unbelievers coming to Him in faith.
John 6:44-57, 59-71
44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
45 It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me. {Not forced, not coerced, not led by God, but they COME unto Him when speaking of the world of believers in general.}
46 Not that any man hath seen the Father, save he which is of God, he hath seen the Father.
47 Verily, verily, I say unto you, He that believeth on me hath everlasting life. [No mention of forced belief.]
48 I am that bread of life.
49 Your fathers did eat manna in the wilderness, and are dead.
50 This is the bread which cometh down from heaven, that a man may eat thereof, and not die. [MAY eat, not FORCED to eat.]
51 I am the living bread which came down from heaven: if any man eat of this bread, he shall live for ever: and the bread that I will give is my flesh, which I will give for the life of the world. [Conditional, based upon the individual's own will.]
52 The Jews therefore strove among themselves, saying, How can this man give us his flesh to eat?
53 Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you.
54 Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day.
55 For my flesh is meat indeed, and my blood is drink indeed.
56 He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him.
57 As the living Father hath sent me, and I live by the Father: so he that eateth me, even he shall live by me. ...
59 These things said he in the synagogue, as he taught in Capernaum.
60 Many therefore of his disciples, when they had heard this, said, This is an hard saying; who can hear it?
61 When Jesus knew in himself that his disciples murmured at it, he said unto them, Doth this offend you?
62 What and if ye shall see the Son of man ascend up where he was before?
63 It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
64 But there are some of you that believe not. For Jesus knew from the beginning who they were that believed not, and who should betray him.
65 And he said, Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.
66 From that time many of his disciples went back, and walked no more with him.
67 Then said Jesus unto the twelve, Will ye also go away? [WILL they want to go away? Not any indication of them being forced by God to stay.]
68 Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.
69 And we believe and are sure that thou art that Christ, the Son of the living God. [No mention of that knowledge having been given the assurance to them by God that Christ has the words of eternal life. They recognized that on their own.]
70 Jesus answered them, Have not I chosen you twelve, and one of you is a devil?
71 He spake of Judas Iscariot the son of Simon: for he it was that should betray him, being one of the twelve.
Two groups are addressed in this context...the general populace of unbelievers willingly placing their faith in Christ, and those who would be His disciples and remain so can only be those who were drawn to Him by the Father. This context DRIPS COPIOUS amounts of revelation for free will of each unbelieving individual has before them in this life. There is nothing in this even hinting at irresistible faith and grace, such as the TULIP doctrine.
But, some will continue with the group-think they have adopted for themselves for various reasons no matter what scripture states IN CONTEXT. To them I say...go for it. We all will answer as to what we have chosen to believe in this life and what we taught to others, for all who teach will be judged doubly for daring to practice teaching doctrine to others.
MM