Twins can be different. Radically so, and on a deeper level we can also have a twin. We must decide how we conquer and channel our animal self for a higher purpose. In Eisav, we have a person who gives way to his impulsive, animalistic hungry persona. He cares only for himself in many ways. Although he still has enough respect for his parents to attempt to deceive them as to his true nature, Rivka knows who he really is and knows that he is unsuitable to 'lead' the Jewish nation or to be its true spiritual father because of how he behaves and uses his G-D given talents.
He is a charismatic person with many talents, a hunter of prey and a trapper of men and he is far from innocent. He pretends to his father that he is though. Rikva knows that such a person is flawed and limited because by their very actions they cut themselves off from real holiness. That is what an aveira does. It cuts you off from the source of truth, dignity and justice. A liar can not bring Moishiah into this world, only truth and on truth with compassion, chesed and justice will the foundation stones of the third beit hamikdash be laid.
Connect to the truth and leave the lies to those who are enslaved by their animal nature. We need to be to have complete trust in the Abishter's chesed and understand that all things are for us to be better people and closer to Hashem and the coming redemption. When it comes is up to all of us.