This would be true if your $4,504 of income was W-2 income and not self-employed income. On a W-2, your employer would pay for 1/2 of your social security taxes owed.
Since you are your own employer, you have to pay your 1/2 of self-employment taxes (SE) on your self-employed earnings of $400 or more. The tax is figured on schedule SE and you do get to deduct part of it (TurboTax calculates it for you).
https://ttlc.intuit.com/questions/1900698-what-is-the-self-employment-tax
https://ttlc.intuit.com/questions/1901205-where-do-i-find-schedule-se
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