If my wife does not work, why can't I claim her as a dependent?

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A spouse is NEVER claimed as a dependent.   File a joint return.  You can file a joint return even if one spouse had little or no income.

If you were legally married at the end of 2024 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $29,200 (+ $1550 for each spouse 65 or older)  for 2024. You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.