Upon termination of lease and vacating the premises, do we really have to have our carpet professionally cleaned?

I don't know the terms of your lease agreement, but most agreements do include a clause regarding carpet cleaning. You are usually obligated to periodically clean it as well as have it cleaned before moving out. If not, the landlord can deduct carpet cleaning fees from your deposit.

But here is where it gets tricky: how long have you lived in the apartment? The longer you live there, the more likely the carpet needs to be replaced for the new tenant. If the carpet shows normal wear and tear, you would not be responsible. But if you haven't lived there for many years, or just to avoid any problems  you may have receiving your security deposit, it may be wise to have it cleaned because the landlord may deduct more from your security deposit than you would pay to have it cleaned yourself.