When over half of the formerly one wage-earner households had two incomes, the price of housing, vehicles, and dangnear everything else went up. While there was a gap in there when people could afford more stuff, it didn't last. There was more money in the economy, and it became worth less. The wages which would have sustained a household just didn't get the same at the store and it became more difficult to get by on just one paycheck.
That is inflation.
That is a coincidence. More people working does not equal higher prices. Assuming they were actually producing something of value, it would mean lower prices. That is, in a free market. Which we don’t have, especially in money. Hence inflation.
Let me put it this way. You seem to be saying that because more people were working there was more money in the economy. Which is a fallacy. You might as well say prices went up because sellers felt like it. It would at least make mire sense.