If Kavanaugh's accuser is lying, why is she the one asking for a thorough investigation?

Because her testimony is supposed to be based on her own recollection, and should not change based on the findings of an investigation.

Not to mention the FBI could not realistically investigate a party that happened 36 years ago, where 2/3 of then principle witnesses have denied it, and the accuser hasn't no idea of the details (where and when) of the party and where there was no contemporaneous claim made to friends or the police.

The investigation is purely a stall tactic because she's scared to go in front of Congress. I don't fault her for being scared since her life will be dragged through the mud, but that's the reality.

The Democrats are to blame for this. They sat on this story and it was a Democratic staffer who conveniently leaked the accuser's name against her wishes at the 11tg hour in an attempt to derail the nomination. The Democrats cynically used this accuser (who may very well believe she's telling the truth).

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