On the other hand, if large parts of your income are tied in near-fixed expenses (e.g. mortgage), then 20% more net income can mean doubling your discretionary spending, and 20% decrease - almost eliminating it.
..and even less if you consider the value of benefits, like health insurance in the US
Why should there be any loss in income?
If you negotiate with management to go from 40 hrs a week to 32 hrs a week, there is usually an expectation you will take a 20% paycut. Parent was saying that since income taxes are tiered, you will likely take a < 20% take-home paycut.