What are three reasons why some people were against the Louisiana Purchase?

The biggest reason people were against the Louisiana Purchase was a financial one. The United States was a very young country and had many debts to pay. When Thomas Jefferson sent envoys to France, they were initially only going to purchase the port of New Orleans; purchasing the the rest of Louisiana required borrowing even more money. Some people (predominantly New England Federalists) argued that the acquisition was unconstitutional and that Jefferson was bending the rules for his own benefit. Really, they were concerned about the economic strain such a purchase might require.
Additionally, the acquisition created problems for the inhabitants of the Louisiana Territory. French and Spanish settlers lived in Louisiana, as well as free black people. The treaty between France and the United States declared that all of these people would be granted citizenship, but some members of Congress did not believe these people upheld American values and therefore did not deserve citizenship.
Finally, Spain objected to the purchase because it did not want the United States to grow even larger. Louisiana had been in the process of transferring from Spanish ownership to French, and when James Madison originally approached Spain about purchasing New Orleans, Spain told him he would have to take it up with France. Spain retracted this argument as soon as it became apparent that the French were going to hand over the territory.
Despite the initial unpopularity of the purchase, fifteen states formed out of the territory. Without the Louisiana Purchase, the United States would be nowhere near the large and powerful nation it is today.
https://history.state.gov/milestones/1801-1829/louisiana-purchase