Why cant he say she is his granddaughter?

I have been with my fiance for 3 years. We have a 6 week old girl. My fiance's father died and his mother remarried 5 years ago. Whenever we see them out, he introduces our child as his wife's grandaughter. I know that they arent blood related, but he is the only grandfather she will know on this side of the family. Is it wrong for this to upset me? Why wont he claim her?