A father making fun of his six-year-old son and saying derisively "you'll never be as good as I am" would probably cause a lot of problems. There's also the alcoholism.

All of this was exacerbated by Jecht disappearing. Tidus was literally left with only bad memories of his father and he outright acknowledges why he clings to those bad memories:

"Even ten years after he left...just thinking about my old man got me angry. But maybe that was just my way of keeping him... Nah."

This is one of my favorite voice-overs from Tidus because it's a perfectly human response that shows how well-written he was. Sometimes resentment and bitterness is better than nothing at all and Tidus is clinging to that because, in the end, he doesn't want to lose his father.

Also Tidus' lack of reaction about finding out he isn't real might have something to do with the pressing issue of Yuna dying any moment now. In short, he had other trout on his mind.

As for why he never talks about it...who would he talk about it to? Zidane could scream and whine at Garland but only the Fayth really know about Tidus and he can't just talk to them any time he pleases.