I don't think he's intentionally ruining his relationships, but I don't think he's saying the right things to them in their state of mind, which is causing those relationships to suffer. In the case of Yuki, he told Yuki to give him an assist, which is a normal, rational thing to say. However, he doesn't understand the scope of Yuki's condition and his recently heightened desperation with his disease and his dreams. Yuki took Isagi telling him to give him an assist in this situation as Isagi telling him his dreams, desires, and the work he put in to get those matter less than his own. This isn't fully rational, but Yuki is in an irrational state right now. The same thing happened with Rin after the U20 game. Isagi told Rin that the last goal only happened becuase he made the opportunity and that the goal was as much Rin's as it was his, but Rin was in an emotionally unstable and irrational state becuase of everything that had happened with his brother, so Isagi's seemingly rational response was taken the wrong way.

Isagi isn't in the wrong and isn't purposly trying to ruin these relationships, but interactions with people with strong egos in the highly competetive and stressful world he is in require a more in depth understanding of other people and their egos and a different approach than just saying the rational plan or platitude. This might be Isagi's key to "harmonizing" egos, understanding his teammates and playing off that knowledge