One reason is that food ingredients are generally safe to ingest, unlike most school lab or workplace chemicals.
Food items often don't contain as much stored energy as lab/workplace chemicals. Turning a standard stovetop to "High" may heat a pan to around ~650 degrees. This is much lower than the temperatures required to melt most metals and many other elements, so the odds of creating an explosion that may send debris into your eyes or perforate your skin is much smaller. Of course, this doesn't make it completely safe, simply safer. If you follow common kitchen safety advice, you should be reasonably safe. Don't add water to hot oil, don't use a malfunctioning device, etc.
When you're wearing safety equipment in a school lab or workplace environment, often you're wearing safety equipment even when it's not strictly necessary, in order to reinforce the habit of using it when it is required. So while you may wear googles, apron and gloves to boil water in chemistry class, it's less about imminent danger, and more about making sure that everyone understands and is willing to use safety equipment properly and consistently.
Finally, kitchen equipment is heavily standardized and regulated, so while accidents can happen, their likelihood is far smaller than accidents in a lab setting. Few people apply direct flame to glass or Pyrex containers in their kitchen. Similarly, it's somewhat easy to clumsily knock a Bunsen burner into a classmate's highly-energetic extra credit project in a school lab.
As for the WebMD numbers, it appears that they're based upon this study. Only a small percentage of the injuries require admittance (20k out of 636k, about 3%, including workplace injuries), and most others are either superficial injuries or injuries to the area around the eye. At 40%, that's 8000 injuries at home that require admittance, with about 30% involving the eyeball itself, and most of those are lacerations that cooking couldn't cause. Burns barely register across all injuries, workplace and home.
So you're pretty safe cooking at home. You'll probably burn your skin from time to time (we all do), but don't let the small risk unnerve you. If cooking was that dangerous, you'd see a lot more people wearing eye patches.