Why is fluorine more reactive than chlorine?
It depends on what reaction you are talking about.


In the context of organic SN1 reactions, the reactivity is $\ce{R-F}$ (least) $\ce{&lt; R-Cl &lt; R-Br &lt; R-I}$ (most). [1] This reflects the leaving group ability, with larger atoms better able to accommodate the extra electron.
In the context of radical homolysis of $\ce{X-X}$ the order of reactivity is $\ce{F2 &lt; Cl2 &lt; Br2 &lt; I2}$ as the sigma bonds become weaker as you move down the period.[2]
In polar aprotic solvents (DMSO) nucleophilicity follows $\ce{F- &gt; Cl- &gt; Br- &gt; I-}$. This order reverses in polar protic solvents due to solvation: J. Chem. Educ., 1970, 47 (6), p 473
Transition metal $\ce{MX_n}$ bond enthalpies have been measured empirically and calculated: J. Chem. Phys., 1957, 26 (6), 1644–1647.. It would be inappropriate to over-generalize, as any discussion here needs to also account for metal oxidation states, HSAB theory, electronic configurations, and ligand-field theory 


References:


Clayden, Greeves and Warren Organic Chemistry, p. 348.
Clayden, Greeves and Warren Organic Chemistry, p. 971.