Neil Young does not even own the rights to his own music. He does get royalties but the catalogue is owned by some other entity. Spotify had no legal obligation to pay any attention to what Neil Young wants.
But they pulled the songs anyway at his request. Terrible for his 12 fans but that is what Neil Young wanted.
Neil Young still owns 50% of his songwriting copyrights. He still can contractually provide guidance on the distribution of his music.
Earlier this month, Young sold 50% of his songwriting copyrights to the U.K. investment company Hipgnosis Songs, which was founded by music industry veteran Merck Mercuriadis. Most of the recordings in Young's discography are distributed by Warner Music Group, though a handful are distributed by Universal Music Group.