Speculation is evidence that represents the opinion, rather than the observation of the witness. That is, a witness who is not an expert must generally testify from personal knowledge, with a few exceptions: laywitnesses can state opinions about things which are within the common experience of an ordinary person (e.g., "He looked drunk"; "She was stacked"; "It was a beautiful sunset").
An email stating that "he didn't like certain schools" could mean that the author was voicing an opinion, based upon other undisclosed facts, that you didn't like to teach in certain schools, in which case the statement does indeed call for speculation, because that's not within the common knowledge of an ordinary person -- or, the statement could be based upon your out-of-court statement, which would be an admission -- and which is an exception to the hearsay rule.
What's really at stake in this letter is that we don't have either the sender or the recipient on the witness stand, so there is no means of authenticating the email as what it is purported to be (obj: no foundation). The witness didn't even get the email from the sender or recipient, so the witness has no personal knowledge of whether or not the email came from the sender or recipient. It could be a complete fabrication (obj: no personal knowledge). The statement "didn't like certain schools" is ambiguous -- it could be reasonably interpreted more than one way.
In every circumstance above, the email is clearly and convincingly more likely to confuse or mislead than it is to probe for the truth, therefore its probative value is substantially outweighed by the risk of counfusion and that means the email is inadmissible, even at the level of a UI hearing.
I don't see how the judge can use that email, so if he does, then I believe you have a pretty strong appeal argument.
Hope this helps.
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