Why are deductions from employees’ earnings classified as liabilities for the employer?

These deductions are made for federal income taxes, and when applicable, state and local income taxes.

Additional payroll-related liabilities include amounts owed to third parties for any amounts withheld from the gross earnings of each employee and the payroll taxes owed by the employer. Examples of withholdings from gross earnings include federal, state, and local income taxes and FICA (Federal Insurance Contributions Act: social security and medical) taxes, investments in retirement and savings accounts, health-care premiums, union dues, uniforms, alimony, child care, loan payments, stock purchase plans offered by employer, and charitable contributions.

So, basically, required deductions go to third parties for things such as taxes, FICA, etc. these things count as liabilities for the employer.

Because that money is owed to the state and federal governments. The employee does not make that payment, the EMPLOYER does. Since the money is OWED to someone, it is a LIABILITY.