At that income level (around 100k/yr), the tax federal taxes reported to you on your last pay stub of the year should be around 28%, when you count FICA (6.2%) and Medicare (1.45%). Add to that whatever your state income tax is (most states have an income tax). As an example, I have to pay 4.63% to the state of Colorado. I think most states that impose an income tax are within a few percent of that. Then add the hidden employer side of payroll tax (another 6.2%), and you end up with a figure that is close to 40% of income.
Minimum standard deduction and a single personal exemption will remove a few percent from this figure at filing time, and you can delay tax payment through 401(k) contribution, but it is still a very heavy tax rate. It is just well hidden from the average income earner by putting the taxes into a number of buckets.
20% sounds low to me too (makes me wonder whether he missed FICA), but add all them together and you're still not giving half your money away.
As tptacek pointed out you are ignoring that the state tax is federally deductible and that the income tax rate at the 25% bracket is the marginal rate.