is there detailed explanation about the hand thing
its lost on me
Most likely a left/right, good/bad superstition, religious, or cultural view. She offered her left hand to greet her the first time they met, and in her mind, it's "bad" in some way, like she's looking down on Oguri, thinks less of Oguri, or views Oguri as being below her. She didn't offer her left hand in respect, but actually in disrespect.
Now, she views that as a mistake, and should have offered her right hand from the start. In her mind, offering her right hand means she respects Oguri, and is genuinely sincere in her words of comradery and friendship.