You are forgetting about self employment taxes, which is around 15.3%. Then you have to pay federal AND state taxes on top of that, which is probably another 25-30%.
If you are a self-employed contractor and you don't have a lot of deductible expenses, you can easily end up paying 40-45% of your paycheck towards taxes.
You also have to account for all of the other expenses that you have to cover without any company help, such as life insurance, disability insurance, health insurance, etc. Plus, you don't really get "paid time off", "sick time", or anything like 401k matching.
Essentially, if you are a contractor who wants to make $100, you need to be actually charging your clients $200.