I usually take a slightly different tack because the technical level of people I usually am dealing with is lower. I tend to be pitching to decision makers and not tech people. A bit of my standard answer is below.
Wix and Squarespace are proprietary systems meant for unsophisticated users who want to build their own websites quickly and easily. While they are good for that specific use case, they do not offer any way to move beyond that if your needs arise. Since they are proprietary closed systems if you need something more advanced at some point your only option is to start over.
WordPress is an Open Source CMS that allows much more freedom. It is not quite as simple to setup and create a new site but if you are talking to me then you are not looking to build it yourself so that is really a non-issue. The main benefit of WordPress is freedom. You can host it on virtually any decent web hosting service and since it uses PHP and MySQL you can have virtually any developer take over a project without problem.
I believe in open source because of that freedom. It is good for me as a developer and it is good for my clients. If something were to happen to me or my company you would have no problem finding another qualified WordPress developer to take over the site in a totally seamless fashion. There would be no need to start from scratch.
Additionally the extensible nature of WordPress means that no matter what your future needs, WordPress can handle it. Adding things like e-commerce and custom quoting systems are just two examples of advanced solution's that I have added to WordPress sites years after they were first built.
WordPress is used by tiny one person businesses all the way up to major websites like the NY Times and I think it is right for this project as well.
