No flaw. The conclusion follows logically from the second premise alone; if even one teacher does not teach biology (this is fulfilled by existence of kindergarten teachers), then it is definitely true that biology is not taught by all teachers.

Wrong flaw. The premises of (B) set up for a potential correct answer choice, but, to match the stimulus, (B) would need to conclude that some non-board members prefer administrative work to teaching.

From the premises, we can validly infer that some/most board members don’t prefer administrative work, but instead, (B) concludes that some board members do prefer administrative work. This isn’t supported; it could be that all of them don’t prefer administrative work and this would be consistent with the premises.

The argument begins with a set relationship (some students prefer X), and combines it with a conditional (if you are in the Calculus Club, you do not prefer X) to conclude a set relationship that overlaps elements of the previous two statements (some Calculus Club members are not students). This commits the same flaw as the stimulus, because we can only validly conclude that some students are not in the club, or that some non-club members are students.

No flaw. (D) validly combines two statements for its conclusion. If (D) had committed the same flaw as the stimulus, it would sound like “some non-principals are advisers to a debate team.”

Wrong flaw. In this argument, we cannot connect the two premise statements, unlike the stimulus. We cannot assume that three o’clock is the same as early or not early. These statements cannot be combined, and so no conclusion can be drawn that overlaps their elements (i.e. popular teachers and coaches).