Mearsheimer provides a direct quote demonstrating NATO's resolve to eventually incorporate Ukraine, which was pledged at the Bucharest 2008 summit.
Bush was also pushing for NATO's membership in 2008 [2].
Mearsheimer's narrative depicts a cornered Russia determined to make Ukraine so politically toxic and disrupted that it would cease to qualify for NATO membership. Therefore, yes, if you say 'Ukraine was never going to get into NATO', that's true after 2010, and more so after 2014. But Ukraine did want to become a NATO member, was promised that it could enter, and had some notable US advocates for membership.
[1] https://www.youtube.com/watch?v=JrMiSQAGOS4 [2] https://edition.cnn.com/2008/WORLD/europe/04/01/ukraine.anal...