Yeah I'm assuming Arata's grandfather probably passed away. Perhaps earlier than he should have.

As for Taichi and Karuta, I think it's more of the fact that he's always done things that he/his mom know that he can win or be the best at. I also believe he likes Karuta but realized the fact that he probably won't ever be on Arata's level like he said so there's no point in trying so hard. But then he sees that Chihaya is having so much fun and that seems to inspire him that perhaps he should just do things for the fun of it and not always worry about being the best.