I don't have a cell phone. People have a lot of questions about this fact, so this page is something of an FAQ specifically about phones.
Yes.
First of all, I have the ability to not carry a cell phone, which is a privilege not everyone has. To answer the question of why, though, it's a privacy thing, but the specifics are likely different from what you're thinking.
Cell phones have to authenticate themselves to nearby cell towers in order to function. This enables location tracking. This data is passively provided to cell providers as a matter of course; collecting this data does not require targeting an individual cell phone to track. I view this as an unacceptable form of mass surveillance, and I am not comfortable being caught up in that surveillance.
If I was going to a protest or something like that, I would not bring a cell phone (or bring one but put it in a Faraday bag), but as a matter of course I don't assume I'm being targeted for surveillance or in an area that is.
If I carried a phone, I could just disable Bluetooth and randomize my Wi-Fi MAC address. These protections would be sufficient for my threat model.
Actually, mobile operating systems have a better security model than desktop operating systems.
Sure, iOS and versions of Android with Google apps are bad for privacy, but I could use something else like GrapheneOS, CalyxOS, or LineageOS.
I would just not install or use those apps.
I think there's a nuanced conversation to be had here. I do think a lot of us have unhealthy relationships with technology, but I also think "phones" get scapegoated in a broad way that isn't super helpful. There are some relevant podcast episodes from You're Wrong About and If Books Could Kill that articulate some arguments in this conversation better than I could. Ultimately, I do think handheld computers offer a lot of utility to people, and I think they're not fundamentally a bad thing.
(Also, not having a phone doesn't absolve me of having an unhealthy relationship with technology. I just have an unhealthy relationship with larger computers rather than smaller ones.)
The short version is that I use bigger (or different) computers for everything.
I'm fortunate enough not to need a phone for work (school) and to never be on call. School communications happen primarily through email. I talk to friends using applications like Signal (for which I use signal-cli and the Electron client). Sometimes I'm unavailable because I'm out somewhere (or my computer is off), and that's actually fine and healthy.
Of course, I need a phone number for some purposes (mostly just listing on forms, but I do have to make a phone call occasionally). I use JMP for this. This service allows me to pay a small fee (6.59 CAD/month) for a phone number I can use via XMPP (for SMS) and SIP (for calls). I considered getting a landline phone plan, but JMP is cheaper.
Whatever mobile app you're thinking of either has some desktop equivalent or other workaround I can use or is non-essential for my life.
If I take the bus, ride my bike, walk, etc. I figure out the directions to my destination and back before leaving. If I drive, I use a GPS device to navigate. This device has a collection of downloaded maps and does not need an Internet connection to work; it just needs to receive GPS beacons to navigate.
I have an old portable media player (a Sansa Fuze+ running Rockbox), which I use to listen to music and podcasts.
Smartphones are basically handheld computers that also happen to be cell phones, unlike older-style flip phones that are cell phones first and have minimal additional features. I actually would get a lot of utility out of a handheld computer; my issue is with the cellular networking. See Why don't you have a phone?