Chrysostom makes a great point. John 6:45 really helps explain John 6:37 and 44. God teaches and we learn, if we choose to, but some choose not to learn. Those that learn from the Father are the Father's. (John 17:6) The Father gives those that learn to the Son. Here are the passages and Chrysostom's comments [emphasis mine]:
All that the Father gives Me shall come to Me, and him that comes to Me I will in nowise cast out.
But perhaps some one will say, If all that the Father gives, and whomsoever He shall draw, comes unto You, if none can come unto You except it be given him from above, then those to whom the Father gives not are free from any blame or charges. These are mere words and pretenses. For we require our own deliberate choice also, because whether we will be taught is a matter of choice, and also whether we will believe. And in this place, by the which the Father gives Me, He declares nothing else than that the believing on Me is no ordinary thing, nor one that comes of human reasonings, but needs a revelation from above, and a well-ordered soul to receive that revelation. (link)
No man can come unto Me, except the Father which has sent Me draw Him.
The Manichæans spring upon these words, saying, that nothing lies in our own power; yet the expression shows that we are masters of our will. For if a man comes to Him, says some one, what need is there of drawing? But the words do not take away our free will, but show that we greatly need assistance. And He implies not an unwilling comer, but one enjoying much succor.
How then, says some one, does the Father draw? This the Prophet explained of old, when he proclaimed beforehand, and said, John 6:45 They shall all be taught of God. Isaiah 54:13
Do you see the dignity of faith, and that not of men nor by man, but by God Himself they shall learn this? And to make this assertion credible, He referred them to their prophets. If then 'all shall be taught of God,' how is it that some shall not believe? Because the words are spoken of the greater number. Besides, the prophecy means not absolutely all, but all that have the will. For the teacher sits ready to impart what he has to all, and pouring forth his instruction unto all. (link)
And He said, Therefore said I unto you, that no man can come unto Me except it were given unto Him from above from My Father.
...when you hear that He has given, imagine not merely an arbitrary distribution, but that if any has rendered himself worthy to receive the gift, he has received it. (link)