I did not say EVERYONE says it this way, of course. I've lived in England, the South US, Western US, and the Southwest, and just about everyone says it the same. I minored in linguistics and while this does not make me an expert by any means, I had to fight for my grade over this issue and the teacher determined that I was correct and his masters student teacher was incorrect in marking me wrong on my pronunciation of it, and that phonetically /chree/ is more common than /tree/. You can determine if you truly say tree, chree or somewhere in the middle by saying a word beginning with a simple T. Like, "Tea." Don't move your mouth once you say tea. Feel where your tongue hits the roof of your mouth to produce this sound. Feel houw your tongue feels and your mouth is held as you repeat Tea Tea Tea a few times. Then say tree, holding your mouth exactly as it was to say tea. Do you do the t first and then the r as a separate, distinct phoneme, or do they merge together to be a sound that is slightly different than the t all by itself. In most people, the sound is not a perfect t-r. It's a combination. It isn't a perfect ch either, but saying it that way at least allows people to attempt to forget the spelling for a minute and think about what the mouth is doing, because when we are speaking of pronunciation, we HAVE to forget spelling and only think of the shapes and positions of the mouth to form a word.

It doesn't matter at all which way you or I do it. There is no right, wrong, better, or worse. I do say something similar to "teach-ree" when I am talking about tea tree oil. But it's just one of those ineresting things to think about, and even when people are clearly saying chree and moving their mouth differently than when they say tea or ree, they will still insist the initial sound is a t. It's just one small way of challenging what we think we know.