Simple. Have you ever read about someone being beheaded on their anniversary? I rest my case.
Heh... This reasoning from WT is ridiculous. In the first account, the chief baker and cupbearer were IN PRISON with Joseph because they "sinned against their lord, the king of Egypt." (Gen 40:1). On Pharaoh's birthday, the cupbearer resumed his duties and the baker was killed. Why? Apparently, Pharaoh carried out capital punishment. The baker did SOMETHING to warrant being put to death. Maybe during their time in prison, it was discovered that the cupbearer was not at fault, so was exhonerated, while the baker had to bear the punishment of death.
In the case of John the Baptist, Herod's birthday was simply "a convenient day" for his wife to carry out her nefarious plans. (Mark 6:21)
Interestingly in the case of Pharaoh's birthday, both the baker and the cupbearer had dreams three days prior that Joseph interpreted accurately. Where did those dreams come from? Where did the interpretation come from? Did God care that it was Pharaoh's birthday, or did God use that fact to attempt to assist Joseph?