An LLC Won't Protect You from Your Negligence
An LLC is a great tool for shielding your personal assets from your business liabilities, but it won't protect you from everything. It won't protect you from your own negligence.
If you run a business where you might injure someone or damage their property if you are negligent, then your personal assets are still at risk for those types of claims, even if you run your business through an LLC or corporation. You might be a fitness instructor, construction contractor or subcontractor, delivery service, software or website developer, security consultant or provider, physician, dentist, lawyer, engineer, architect, or any other type of service provider whose negligence might harm people, their property, or their business. The law will not let you hide behind your entity when you are personally negligent.
You protect yourself from those risks by buying appropriate insurance (e.g., malpractice insurance, errors and omissions insurance, or general liability insurance).
This doesn't mean your LLC is useless. It still protects your personal assets from other business liabilities. It also has other benefits (see https://www.joelankney.com/blog/i-prefer-llcs).