I've seen this argument many times, but as someone else who has done a lot of both, I've never really understood it. It's just programming, like any other software project. Sure, you might use different languages and each might have its own tool chain, but unless you're using radically different languages or tools in the two cases, those are probably superficial differences. Most experienced professional developers can probably work in several languages, and you pick up a new tool chain in days if you need to. But the fundamentals of programming are still much the same whatever you're building. Certainly different applications also have different knowledge and skills -- writing a business automation tool is likely to be quite a different experience to writing a control system for ABS in a car, say -- but for a typical web app, the front and back ends are usually going to overlap a lot in this respect.

As I mentioned in another comment, the huge exception to this is junior roles, because at that stage in someone's career they probably haven't gained much diversity of experience yet and you probably should start by focussing on one particular aspect. So if your project team consists of many relatively junior people and not so many seniors with broader experience, sure, you're going to put most people specifically on front-end or back-end, at least to start with.