> since the half the employer pays is not included in your net income
There is a total cost for employer for a particular employee and the take-home pay for that employee. Where between those two we put a number that's called "your net income" is just arbitrary convention.
Employer knows how much the total cost will be when they negotiate the salary. It's all the same to them if the entire amount goes to you personally and then you use it to pay health insurance, or they first pay some of that amount to health insurance and then give the rest to you.