Until about two years ago, I didn't have a cell phone. I did get a bit of mild teasing from people when they asked for the number and I had to admit that I didn't have one.
But now that I have one, I never give out the number. Partly because I can never remember it. But mostly because once someone has the cell number, that is the only way they will try to contact me. And that's a bad choice on their part and it means that I will most likely not get their message on time.
The cell phone is for me and my convenience. It's for emergencies. I have a pay-as-you-go plan, so I do not use the cell for long conversations. Its real purpose is to be there as a means of communication if my car breaks down or I'm stranded somewhere.
So the cell is usually not where I am. It's in my purse in the living room, while I'm back in the kitchen. It's in the kitchen charging, while I'm out running errands. It's turned off a majority of the time. I use it about once a month. About once a week I remember to charge it and check for messages. It is really not a good way to try and contact me.
I can give people a home phone number and a work phone number, home and work email addresses. That's 4 different ways to get ahold of me. That really should be enough. And yet, like the OP, people and offices simply won't take, "Oh, just use my home phone," as an answer. I've started saying, "I don't have a cell phone," out loud and adding, "that's available for you to use," silently in my head.
Right now, I'm struggling to get a good friend to stop using the cell phone every time she wants to reach me. About a month ago, I was headed out to her place and was stopped for almost an hour by a bad traffic accident. I called her on the cell phone to let her know that I would be late. So she got hold of the cell number and has used nothing else since, despite repeated attempts on my part to convince her that I don't use the cell very much. She got very angry at me at one point, because she thought I was ignoring her. No, I was just not checking the cell. How many times do I need to say that to convince her to go back to using my land line number? She tells me I need to enter the 21st century and use my cell, but I just don't want the added hassle.