Why is the first halogenation the slowest one?
The first halogenation is the slowest because the first radical intermediate is the highest in energy.
I think you may be asking about the successive free radical halogenation of a molecule like methane:
CH₄ → CH₃Cl → CH₂Cl₂ → CHCl₃ → CCl₄
The corresponding free radical intermediates are
·CH₃, ·CH₂Cl, ·CHCl₂, and ·CCl₃
The Cl atoms stabilize the radicals. The more Cl atoms, the more stable the radical is.
The diagram below works just as well if you replace OCH₃ with Cl.
So, breaking the C-H bond in CH₄ to form a carbocation takes the most energy. It is the slowest reaction.
Breaking the C-H bond in CH₃Cl takes less energy, because ·CH₂Cl is lower in energy. This step will be faster.
The formation of CCl₄ from CHCl₃ will be the fastest of all.