Technically, there isn't anything wrong with WordPress per se, but it gets bloated quickly with potentially poorly coded plugins. If you feel that WordPress would work best for you, go for it! However, the VPS I'm using is on the lower end of RamNode's offerings, which makes reliably hosting PHP and MySQL a bit of a challenge.
When I finally bought AntonMcClure.com, its original website used PHP and read data from static files. While this was slightly better, generating pages used considerable amounts of CPU and RAM, and a lot of URLs were unnecessarily ugly or inconsistent. The new website engine fixed many of these issues, lead the way to future improvements, and comes partially with a feeling of accomplishment from being made from scratch.
Why You Shouldn't Use WordPress
Security: WordPress isn't exactly the most secure. Many WordPress installs are automatically vulnerable when new exploits are found, with some of these installs not being regularly updated.
Updates: The WordPress team does release regular security updates, however installing them all may be time-consuming and comes with a risk of your themes, plugins, or entire website breaking.
Plugins: While plugins let people build upon WordPress, many plugins have known issues that are never getting fixed. A lot of these plugins get released for free, and then their developer either stops maintaining it or forgets about it. Now, many people would be running an insecure plugin opening their websites to more vulnerabilities. There is also the issue of malicious plugins adding things like backdoors, granting potentially unwanted users access to administrative features, spying on users, and so on. Like with any software or service, not just WordPress, you need to be careful with what you install.
Features: Even if you don't have issues with malicious plugins, there will come a time that a plugin doesn't do what you need it to do, does "too much" such as adding unwanted features to your website, or you have just reached the end of WordPress' capabilities. You now have to make a choice: choose similar plugins and hope they work, write the plugin yourself from scratch, or start over and hope you can make the website work this next time.
Speed: Regardless of what plugins you have installed, if PHP or MySQL requests get overloaded, your site will slow down a ton or become completely unavailable. The more plugins you add, the more code WordPress needs to process on every page load, meaning your site will become slower and slower, and you will reach your server's system resource limit quicker.
Search Engine Optimization (SEO): Search Engine Optimization on the modern Internet is necessary for getting good page ranking. Unfortunately, WordPress doesn't use the best SEO practices. While SEO plugins exist, many being free to get, essential features remain limited to paid users. If you're going to pay for an SEO plugin, it would be better to pay professionals to make a custom website, with better and fine-tuned SEO.
Compatibility: Ever see a website that looks good on some browsers but not others, or looks good on desktops but tiny on mobile? Many custom themes on WordPress still have this issue. There may also be issues with the HTML and CSS code, which would show in validators such as validator.w3.org, but not get fixed by the theme's creator.
Themes: Compatability issues aside, many free WordPress themes look too similar to each other and may look unoriginal or generic, and may include paid functions. If you want a design based on your site's needs, you will need to pay a web designer for it. If you're paying for your theme, it would be better to pay professionals for a custom website.
Alternatives to WordPress
There are several alternatives to WordPress you could consider. Some of these include:
The above list certainly isn't every CMS or static site generator out there. If none of them work best for you, nothing is stopping you from doing what I did, and write a custom CMS or static site generator. Regardless of what you use, make sure to pick what works best for your specific use case, and that you have it set up securely.