Why I don't use Spotify:
Local streaming > Online 3rd party app streaming
There are heck lot of methods for Spotify while there aren't any for Apple Music which is superior quality.
Spotify is focused for Android and just isn't good(gonna explain later). Not just Spotify, I don't recommend any online music apps unless you're a fan of low quality battery draining 3rd party apps.
Doesn't have lossless audio. This should probably be #1 reason, but meh.
Uses 320kbps mp3 tracks for streaming which is "normal quality" plus you get that only on "Spotify premium". Normal quality at a price.
Spotify for music is like Crunchyroll for anime. Most of the time, you don't get what you're looking for. Some tracks are only available for Apple Music, not for Spotify. And just like Crunchyroll gives you censored short library of anime. Spotify give you normal quality short library of tracks.
Default stock apps > 3rd party apps. You can actually this yourself. Play a quality song from your local library via Play Music(if you're on stock Android). Then play the same song via Spotify online library. You can do your own setup to test for quality difference. I have personally tested it on Bluetooth speakers. Local must sound louder and better than the latter.
Many other reasons, but I'll mention them later on when somebody tries to argue these.