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Why does the addition of 50ml of 0.5M NaOH to 50mL of 0.6M KOH cause the pH to decrease (aka more acidic)?

Because you have reduced the (OH^-) of the 0.6 M KOH by adding an equal volume of 0.5 M NaOH
50 mL x 0.6 M KOH = 30 millimols. pH = 13.78
Adding 50 mL x 0.5 M NaOH = 25 millimols NaOH added
30 millimols + 25 millimols = 55 millimols
55 millimols/100 mL = 0.55 M. pH = 13.74.
Actually, diluting with an equal volume of a less basic solution of NaOH effectively averages the 0.6M and 0.5M to 0.55 molar and 0.55 M is more acidic than 0.6 M (but not by much).

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