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I think that when you remove the first electron that is unpaired, the second electron will be in a lower orbital and will be paired. Since it is paired, it requires more energy to remove it and is therefore harder to remove.
You can think of it like you are making an atom that is already more positive than it should be, even more positive. It will be harder because the atom wants to keep that electron and you are taking it away from its stable form and the form in which it has no net positive or negative charge.
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