A conclusion, according to the definition stated in one of the previous lesson, is "A statement which is supported by another statement." The author is making the statement "I'm going ahead with the operation". This statement is supported by his reason, another statement a/k/a the premise, "With my current medical condition, there may not be another alternative."

The latter supports the former. We do not know if undergoing this operation is the right decision, as we don't know what this operation is and nor did the author state they're a doctor. All we know is that the author argues that he has no choice but to go with the operation, because of their medical condition and there's no other alternative. Structurally, this is considered an argument because it has the premise + conclusion.

I thought the same thing, but I re-read the passage and noticed that the statement in the conclusion "as a teacher" is supported by the statement in the premise "based on my experiences". The author points out that, because he is a teacher, he believes that students accessing academic records would be a blunder, and then uses his observations in the second premise to support this claim. So the "as a teacher" would make sense to be part of the argument.