Why your tax isn't a flat percentage
US federal income tax is progressive: income is taxed in slices, each at its own rate from 10% up to 37%. Only the dollars inside each bracket are taxed at that bracket's rate. First, the standard deduction (or your itemized total) comes off your income to get taxable income; then the brackets apply.
That's why two people in the same "tax bracket" can pay very different effective rates — deductions and where your income lands in the slices matter more than the headline bracket.
Getting a raise into a higher bracket never lowers your take-home — only the dollars above the threshold are taxed at the higher rate.