In the US, there's a Social Security payroll tax (previously 12.4%, now 10.4%) that's split between employer and employee. Self-employed people pay it themselves; their clients don't.
I think what he meant was that you have to consider a hefty tax burden come April 15 because, as a contractor, you don't get taxes taken out of your paycheck. This is where having a good accountant and knowing what expenses you can deduct comes in (to reduce your taxable income).
If for nothing else, you should have a business just so you can claim more expenses and reduce the amount you have to pay Uncle Sam (from my understanding, all you need to have is a profit motive -- not necessarily profits).
My tax guy always tells me: the US hates employees. There are more loopholes if you contract or (even better) have your own business (which could be a contracting business).
Plus you don't get taxed at source so you can take that extra 30%+ you get each paycheck to pay a tax person to figure this all out for you in time to save up for the tax hit at the end of the year.