Draw the product for the chlorination of 2-methylbutane that proceeded through a secondary radical.

Because of the great reactivity of the chlorine radical, abstractions of primary, secondary, and tertiary hydrogen atoms are all exothermic. Therefore, the stability of the product radical has less influence on the activation energy of the reaction. Thus, according to the Hammond postulate, the transition state is more reactant-like.

According to R. Brückner Advanced Organic Chemistry, the chlorination of isopentane has four monochlorination products:

22 % 2-chloro-2-methylbutane 33 % 2-chloro-3-methylbutane 30 % 1-chloro-2-methylbutane

15 % 1-chloro-3-methylbutane

The statistical factor is responsible for this.
If each hydrogen atom of isopentane could be substituted at the same rate, the ratio would be

1 hydrogen atom (8 %) → 2-chloro-2-methylbutane 2 hydrogen atoms (17 %) → 2-chloro-3-methylbutane 6 hydrogen atoms (50 %) → 1-chloro-2-methylbutane

3 hydrogen atoms (25 %) → 1-chloro-3-methylbutane

In terms per hydrogen atom, the experimental yield is

22 % / 1 = 22 % → 2-chloro-2-methylbutane
33 % / 2 = 16.5 % → 2-chloro-3-methylbutane
30 % / 6 = 5 % → 1-chloro-2-methylbutane
15 % / 3 = 5 % → 1-chloro-3-methylbutane

Thus, 2-chloro-2-methylbutane is indeed slightly preferred – as you have expected.

I got CH3-CH(CH3)-CH(Cl)-CH3

But my professor responded saying "At least one of the atoms in your response has an invalid valence. If you don't see an atom underlined in red, look for an atom that violates the octet rule, or try expanding your shortcut groups."

Any help?

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