No, you are not reading the words as they are laid out. Nowhere in the text does it say that all men are then recognized as equals in the eyes of the law. To claim that was what they had asserted is just dishonest or stupid. Why would Jefferson have put this in the first draft if he was asserting the nonsense you put into his text?
He has waged cruel war against human nature itself, violating its most sacred rights of life and liberty in the persons of a distant people who never offended him, captivating & carrying them into slavery in another hemisphere or to incur miserable death in their transportation thither. This piratical warfare, the opprobrium of infidel powers, is the warfare of the Christian King of Great Britain. Determined to keep open a market where Men should be bought & sold, he has prostituted his negative for suppressing every legislative attempt to prohibit or restrain this execrable commerce. And that this assemblage of horrors might want no fact of distinguished die, he is now exciting those very people to rise in arms among us, and to purchase that liberty of which he has deprived them, by murdering the people on whom he has obtruded them: thus paying off former crimes committed again the Liberties of one people, with crimes which he urges them to commit against the lives of another.