My wife made almost $20,000 last year as a part-time employee but they withheld almost nothing out of her paychecks for federal income taxes. Why?

[xmasbaby0]

That would be a question to ask the employer.  What did she put on her W-4 at work?   Sadly, there is nothing to do about it for your 2021 return, but going forward she needs to change her W-4 at work and have tax withheld if she is a W-2 employee.

https://ttlc.intuit.com/community/tax-topics/help/what-to-know-about-the-new-2020-irs-form-w-4-emplo...

https://www.irs.gov/pub/irs-pdf/fw4.pdf

https://www.irs.gov/individuals/tax-withholding-estimator

[ColeenD3]

The only way to know his reasoning is to ask the employer. However, it could be due to some entries she made on her W-4. One such reference encourages this:

How should married couples complete W4?

Your spouse should claim all the allowances that the Two-Earners/Multiple Jobs Worksheet says you, as a couple, are entitled to claim, and then you would claim zero allowances on each Form W-4 that you complete for your two jobs.   W-4

Another possibility is that someone who works part-time had a lower weekly/biweekly salary. Employers go by a chart the IRS publishes that tells them how much to take out based on the income and the exemptions on a W-4. If the income is low, the withholding is low.