If the IRS says more of your SS is taxable it might be because they changed and increased some other income on your return. Read the letter again. A common change is they increased the taxable amount of any 1099R you got for Pensions, and 401k or IRA withdrawals or conversions.
And if you reported your pension or IRA on the wrong line the IRS might miss it and say you didn't report it. I would check for those. IRAs go on 1040 line 15 (1040A line 11) and Pensions and 401k go on 1040 line 16 (1040A line 12). And Make sure you got the right taxable amount on the “b” line.
All of your SS is not taxable. Only up to 85% of Social Security becomes taxable when all your other income plus 1/2 your social security, reaches:
Married Filing Jointly: $32,000
Single or head of household: $25,000
Married Filing Separately: 0