When Izuki was very young his sister told him a very funny basketball pun. That was his start on the path of becoming a basketball player.
Unfortunately, Hyuuga had made him promise to never tell that story again 'on account of how awful the pun was'. Hyuuga has no culture in his soul, but for the sake of their friendship Izuki does his best. He never told his sister though, because she still thinks well of the team not knowing that not a single one of them appreciate puns properly. They just can't get into the zone.
But then, that's why Izuki always does what he can to enlighten the rest of the team, to better help them to understand the greatness of puns and brighten their life. Kuroko especially can really use some good puns to ignite his existence.
It's not that Izuki isn't properly sympathetic to Kuroko's plight and his whole thing with the Generation of Miracles; but for Izuki – who turned to basketball to be able to communicate with his peers when puns could not cut it, they just didn't appreciate his razor wit – Kuroko's problems of not being able to communicate with his ex-teammates through basketball isn't very relatable.
Still, Izuki will do his best to assist Kuroko on their path to the Winter Cup, since they'll have to fight through the Generation of Miracles anyway. Playing basketball together to the top: that is the language of Seirin's basketball team. At least they all have that in common.
It doesn't matter, one day someone will understand the big picture when it comes to the art of puns. Until then, there's always basketball.
Hey Shun, listen to this one: basketball players may not be able to control their saliva but just look at that dribble power.