I never was fond of Izzy (though he was nice in 02), but Tai was a great character ^^
Oh, if you ever want to understand Matt (Yamato); let me know
I think I know enough about him to explain - the original Yamato, at least. The producers sometimes were contradictory to themselves, but I go for the original, means the 01 Yamato.
The basic story is: Matt loves and has always has loved his little brother more than anything else in his life. When their parents divorced, Matt lost his little brother as well as this mother. That hurt him very very much. He never wanted to get hurt like that again, so he shut himself off, not letting anyone get close to him so he wouldn't lose anyone again someday.
Also, his biggest duty - in his own eyes - is protecting TK. So he tries to be strong - never crying, never showing weakness, so TK won't be worried. No matter how much Matt suffers, he tries not to show so TK will be happy and feel safe.
Of course, I don't know which sub you saw. I talk about the Japanese version. In the American one, they messed up Matt's and TK's relationship entirely, and I can't explain you Matt's personality there
He never called TK 'squirt' or treated him mean in the version I watched. TK was actually the only one who knew about the 'true' Matt - and also knew how much Matt loved him ^^
That's it I think. I hope I didn't get on your nerves now.