Webcam, smart phone? When some people see themselves in profile, they think that they need a change in appearance. One of the things that might be noticeable with newer imaging devices is a "receding" chin. If there is micrognathia, then having plastic surgery is one option for dealing with it. I suggest that patients consult an experienced board-certified cosmetic or plastic surgeon if concerned.
Jobs & focus on face. The rise of internet webcam and specifically the "facetime" applications where not only others but self visualization of the transmitted image especially when tucking your chin makes this a particularly recent phenomenon as individuals use smartphones/webcams/electronic imaging for communications, dating, conferences, job applications. A strong jawline conveys youth and strength and confidence.
Interesting question. The standard explanation is that the rise in videoconferencing (vc) has lead people to think they have weak chins. Many factors might feed into this, including the focal lengths of the lenses used for vc, the fact that the lenses are usually looking up at your face. There are good indications for chin augmentation, either with implants or bony advancement: all the facial relationships matter here.
Genioplasty. Many folks with chin deficiency are becoming more aware of appropriate treatment alternatives, and more are aware of what cosmetic surgery can accomplish. I generally recommend a true sliding genioplasty, an osteotomy of the chin, rather than an artificial chin implant. The cosmetic results are superior and you don't run the risks associated with silicone or other artificial implants.
Face time. As more and more people use their smart phones, ipads, and computers for online video chat, they now see themselves from the unflattering viewpoint of the webcam. This has prompted many people to see their plastic surgeon to consider chin implant surgery.
Vanity. Vanity and looking like the movie stars.