From the given information, we can deduce the following:

1. A is between D and F.

2. C is opposite D.

3. D and E are not on neighboring chairs.

Based on these deductions, we can determine which statement must be true:

A is opposite B: We cannot determine the exact positions of A and B, so we cannot conclude that A is opposite B.

D is opposite E: We cannot determine the exact positions of D and E, so we cannot conclude that D is opposite E.

C and B are neighbors: There is no information provided about the positions of C and B, so we cannot conclude that they are neighbors.

B and E are neighbors: Since D and E are not on neighboring chairs, and C is opposite D, it means that B and E must be neighbors in order to satisfy the given conditions. Therefore, the statement "B and E are neighbors" must be true.

Hence, the correct answer is "B and E are neighbors."