It seems to me that you would have to show from John 6 that being drawn to Jesus by the Father
necessarily results in coming to/believing in Jesus, hence the drawing grace of God is irresistible. Outside of an a priori approach I haven't yet seen how this passage would teach such.
Understanding that 'coming to' and 'believing in' are the same thing we can observe the following:
For irresistible grace to be taught in John 6, it must show:
This set of people - - - - - - - - - - - - - - - - In this category
All those drawn by the Father - - - - - - - - - believe in Jesus
What we can understand from John 6:
This set of people - - - - - - - - - - - - - - - - In this category
None can believe - - - - - - - - - - - - - - - - unless drawn
Those not being drawn by the Father - - - - - Cannot come to Jesus
The legitimate understanding of this is that if you believe in Jesus then the Father has drawn you.
While this is true:
This set of people - - - - - - - - - - - - - - - - In this category
All who believe in Jesus - - - - - - - - - - - - - drawn by the Father
John 6 does not teach that:
This set of people - - - - - - - - - - - - - - - - In this category
All those drawn by the Father- - - - - - - - - - believe in Jesus
I'm so far convinced the idea that
"all those drawn by the Father necessarily come to faith in Jesus" isn't taught or supported in John 6. I'm not saying it's not a true statement, just that it's not supported in John 6. For a better and more thorough case you can
reference Dr. Barry Creamer's blog post.