Like many of his predecessors, John Q. Adams had an intense rivalry and almost personal hatred of the man who would defeat him after one presidential term- Andrew Jackson.
Q. Adams was a Puritan, one of the last well known gentlemen from the 'deferential age', was Harvard educated and steeped in the classics.
Andrew Jackson was self taught, had not been to school, and was a frontiersman that had fought in two duels and had a bullet lodged near his chest to prove it. He was what the Romans would have called a 'new man'- someone that came from obscurity but rose to a high political rank.
Even beyond the difference in backgrounds, Jackson's political beliefs were about as different as possible from Q. Adams. Where Q. Adams saw a mob, electioneering and backwardness, Jackson saw democracy.
Jackson ran against Q. Adams when Q. Adams won his first term and lost. Jackson called it a 'corrupt bargain' and blamed Q. Adams for essentially going against democracy and making political bargains with Henry Clay to secure the presidency.
During the election after Q. Adams first term, things got very personal very fast. Jackson was called a bigamist (when he married his wife, she was technically still married to another man) Jackson took offense to this and his wife, who had a very hard time enduring these kinds of politics ended up getting sick and dying.
Jackson personally blamed Q. Adams, although it was most likely political operatives that he wasn't directly controlling that caused these accusations to be published. Q. Adams wanted to explain his position to Jackson after the election in D.C., but Jackson never bothered to 'call' on Q. Adams which was a big deal and big time snub to a gentleman of those days.
Q. Adams, like his father with Thomas Jefferson, ended up leaving D.C. in the middle of the night rather than staying in Washington to view Jackson's inaugural. There were only three presidents in all of American history to do this, and one was Q. Adams' father.
On not attending the Harvard award ceremony of an honorary degree to Jackson, Q. Adams said " As an affectionate child of our Alma Mater, I would not be present to witness her disgrace in conferring her highest honors upon a barbarian who could not write a sentence of grammar and could hardly spell his own name."