He wanted to have some kind of control over the new president's actions. So he didn't believe he could managed to persued John Adams. He wanted to imposed his own vision of America on the nation. He could influence Thomas Pinckney more. Also there was some badblood between them.
Hamilton did not trust he could control Adams to the degree he could impact Thomas Pinckney, the other Federalist applicant. Adams had contradicted war with France, which Hamilton had generously bolstered, so this may likewise have been a factor.
The best clarification is that Hamilton wished to be the power behind the position of royalty, and force his very own vision of America on the country. He had made an excessive number of foes amid the Washington Administration to be chosen in his own right; so he wanted to remain an informal power intermediary. Adams was unreasonably autonomous for Hamilton's taste.
Hamilton's intend to get votes in favor of Pinckney faliled, and the result was Adams becoming President and Jefferson Vice President.
