Haha. Wait he actually thought that was an invitation.
Gatsby vs Self
I love you both!
In this panel Tom and Myrtle are having a fight. They are both drunk, and Tom doesn't think Myrtle has the right to say Daisy's name. Myrtle taunts Tom by repeatedly saying Daisy's name. Tom snaps and punches her in the face, breaking her nose.
Gatsby, who did not grow up around the wealthy, doesn't always know the proper etiquette when he's with them. The Sloanes rhetorically ask him if he wants to go to dinner with him. He accepts, because he doesn't realize their invitation was insincere.
Daisy is conflicted. She has to choose between her true love Gatsby, and her life with Tom. Ultimately, she chooses the status and security Tom provides for her.