Seiji could only tell Yui a limited amount of information without revealing his ability to travel back in time.
If it was truly necessary, Seiji was resolved to tell Yui about his ability. However, he wanted to avoid doing so if possible. He had a premonition that telling her about his ability might result in something completely unimaginable.
Even without his premonition, he found it difficult to trust Soul Society as much as he had before he personally witnessed the destruction wrought in the city.
Although he'd never trusted Soul Society that much to begin with, the fact that Soul Society hadn't been able to stop that catastrophe made him trust Soul Society even less.