A midpoint divides a segment in two congruent halves. To show this we typically use hatch-marks, where the number of marks identifies which segments are congruent. We see two examples of this below.
Let's look at the given diagram.
Visually, it looks like DM≅ MB and AM≅MC. However, mathematically, this is not what the diagram tells us. Interpreting the diagram, we see that DM≅MC and AM≅MB.
Therefore, point M does not cut the two segments in two congruent halves, which means it cannot be the midpoint.
