It is a lie that your employer pays 1/2 of Social Security and Medicare taxes. Ask someone who is self employed who pays these taxes and you will learn the answer. The answer is the person working.
You are working for your employer and you must generate more value for your employer than he expends in employing you. If you do not succeed in this then one of 2 events happens. You are fired, or the employer goes out of business. Thus the law keeps you ignorant of who really pays these taxes.
To illustrate the point an employer must pay $100 to employ you. That is his total cost in taxes and wages. Now the accounting gimmicks come into play. Instead of you earning $100, you and the employ say you "earn" $85.