I would not agree that there is "no evidence" that Jefferson reduced the size of the military. For example, I quote from the link below:
With the expert help of Albert Gallatin, secretary of the treasury, and James Madison, secretary of state, he greatly reduced the army, the navy, and the foreign diplomatic corps.
I also quote from America: A Narrative History by Tindall and Shi:
The basic formula was simple: cut back expenses on the military. A standing army menaced a free soceity anyway. It should therefore be kept to a minimum... The navy ... ought to be reduced further..." (pp. 376-7 in the 5th edition of the book).
I further quote from The American Pageant by Bailey, Kennedy, and Cohen.
Jefferson reduced the military establishment to a mere police force of 2,500 officers and men. ... Accordingly, Jefferson shrank the navy to a peacetime footing.
These constitute, in my mind, evidence for my contention that Jefferson shrank the military.
The above answer is not sufficient to explain Jefferson's reasoning. Jefferson never expressed a distaste for war; in fact he had no qualms about blockading the port of Tripoli and sending American forces to battle the Barbary Pirates. Had Jefferson believed the U.S. was capable of withstanding a war with Britain,and had Congress been in session,he would have had no choice. Not only that, under the constitution, only Congress, not the President, can declare war. At the time of the Leopard-Chesapeake incident, Jefferson was not inclined to call Congress back into session for a declaration of war. There is also no evidence that he "reduced the size of the military," as at the time, the U.S. had no standing army. War fever was high after the incident, so much so that one Federalist described Jefferson as
A dish of skim milk, curdling at the head of our nation.
In fact, Jefferson had followed the same policy of John Adams before him who had threatened to resign if war were declared against France, and Washington, who had issued a Declaration of Neutrality. His decision was based on precedent and policy, not because of his personal feelings.
There are a number of reasons that can be given for this.
First, Jefferson did not like the idea of war in general. He very much preferred to use "peaceful coercion" like the embargo that he later imposed.
Second, and perhaps most importantly, Jefferson did not believe that the US was truly ready for a war. Jefferson had reduced the size of the US military because, as a Democratic-Republican, he wanted a smaller government. However, this left the US weaker than it would have been. Of course, Great Britain was the most powerful country in the world and so the war would have been unequal no matter what.
Between his preference for peace and the weakness of the US military, Jefferson declined to ask for war in the aftermath of this event.