Why is the h in PhD lower case?

The lowercase "h" in "PhD" is a stylistic convention reflecting the abbreviation's origin and the grammatical function of "doctor" in the full term "Doctor of Philosophy". It's not a hard-and-fast rule, but a widely adopted practice.

Essentially, it's treated as an abbreviation where the initial letter of a postpositive (a word that comes after the noun it modifies) is lowercase, while the others are uppercase. Similar abbreviations follow this convention (e.g., MA, BA, etc.). The "Ph" represents "Philosophy" which is postpositive to the noun "Doctor."