More than likely, his homosexuality. It was a known quantity, and a thing that people regarded with great disdain until recently, for all the obvious reasons. It's even the title of a short opera about the last days of his life that premiered in 2017, Michael Finnissy's "Shameful Vice." The Soviet government worked extremely hard to purge the historical record of any indication of Tchaikovsky's sexual orientation, thus making scholarship difficult, and it is a trend continued by the current Russian government, unfortunately -- it's almost inevitable, if tragic, when the most cherished composer of Russian classical music is queer and queerness is incompatible with the official governmental stance of Russia.

Some good references on Tchaikovsky's sexual life: Poznansky, Alexander, Tchaikovsky: The Quest for the Inner Man (New York: Schirmer Books, 1991); Poznansky, Alexander, Tchaikovsky Through Others' Eyes. (Bloomington: Indiana Univ. Press, 1999).