You have to think carefully about how to clean up your object if something throws during its constructor, and throwing an exception in a destructor can lead to your program aborting if that destructor was called as a result of another exception being thrown.
Note that I don't think banning exceptions is really the answer; in particular, the destructor issue is just a specific case of "handling errors during finalization is really hard", and you can't get away from finalization in general. Exceptions really put those issues front and center, though.
Oh, exceptions during construction/destruction, right. I don't think Go addresses that at all. Go's defer is just like a finally block, and panics can happen at any time.