baleares,
As I see it, the reasons why you don't get on don't matter. You don't get on, so this chap is not a good instructor for you. And....he lied to you! I see that as enough reason not to want to fly with him, putting everything else aside.
The CFI may be busy, but he won't want to lose a student to another school. Ask if you can fly with him, at any time that's convenient for him, and be prepared to wait. Don't be fobbed off with "busy"; it's an excuse. I've had busy instructors, and I've been a busy instructor, and you can fit people in at some point if it's necessary. I bet he'd rather do that than have you leave! I suspect he's just trying to give the other instructor some students, but you probably don't have to go along with that if you don't want to and insist that you can't. And don't worry about a bad atmosphere; this is your money and your decision.