If it really is unusual in your profession, I'd resist it, but I'm surprised that any profession has managed to resist the tide of 24/7 contact culture!
I guess only you can answer this one - is your career going to stall if you say no? Are you going to get a reputation for being unhelpful/ not a team player/ not loyal to the company?
Alternatively, do they want your number because there are issues around handovers/ infornation transfer or other problems that result in loss of productivity/ client handling issues etc? On your part or on the part of others who are complaining it wouldn't have happened if they could have phoned you?
What's the context of them asking? Is it arising from a specific situation?
You really need to give them an alternative solution if this question has come out of a situation where there was an issue.
But really, if the answer to all of those questions is a no, and there really is no underlying issue or negative perception about your work image, then I'd carry on as you are enjoying it whilst you can :)
Ps you wouldn't even get a job in the field I work in if you refused to give contact details, and no, it's not life and death, it's just the way the industry works. People have started to put 'out of office' on their emails when they are in lots of meetings and might only be able to check mails once an hr. Bonkers! But I'm sure I'll have to join in soon...