Should one carry mobile phones in our pockets, or in our hand luggage, during an airport security check? Why?

It is safe to carry phone in pockets and not in handbags as it might get stolen, if kept in handbag.

At one time (it's a long story) I had to pass through airport security about a dozen times. This was well before 9/11 and those body X-ray scanners didn't exist. I was wearing a heavy leather jacket with metal fastenings and carrying a large quantity of keys on a heavy chain, along with many other metallic objects. It was easier to take off the entire jacket and stick it on the X-ray belt, walk through the metal detector and get hand scanned for belt buckle, and then put the jacket back on. While at Uni, it was common for people to wear cell phones on neck lanyards; I still do this. After however many years, I still haven't dropped and cracked it etc., despite its age and the need for a factory reset to clear out some junk. Even in the course of my normal employment around that time, similar security was common at City Court Houses and I adopted the practice of removing the jacket and letting them X-ray the whole lot. If something was questionable, I had no hesitation in pulling out whatever was required, but it sure saved much time over emptying pockets and refilling them.