The Democratic-Republican Party was formed primarily due to Thomas Jefferson's clash with Alexander Hamilton on a number of issues. Jefferson and Hamilton had fundamentally different visions for the future of the United States, particularly regarding the role of the federal government, economic policy, and foreign relations. Jefferson favored a more agrarian society with a limited role for the federal government, while Hamilton advocated for a strong central government and an industrial economy.
While Thomas Jefferson indeed sought to promote particular values and beliefs through the formation of the Democratic-Republican Party, it was largely a response to Hamilton's policies and the Federalist Party's dominance in the early years of the republic. Jefferson's party aimed to represent the interests of farmers and advocate for states' rights against what they perceived as the overreach of federal authority embodied by the Federalists.
So, the most accurate reason from the options provided is that "Thomas Jefferson clashed with Alexander Hamilton on a number of issues."