Let's break it down:
Do you have to be a pro to ride a Harley? No, BUT...Harleys cost a lot of money, so it's not usually a good first bike for a new rider. There are two types of motorcycle riders -- the ones who have dumped their bikes, and the ones who are going to dump their bikes. Harleys are notoriously expensive to fix, so you may want to consider starting off on a bike that won't cost as much up-front and is cheaper to fix and maintain, especially when you consider the fact that your first bike is bound to get dinged up quite a bit while you learn to ride.
Do they need a lot of care? If you want to keep a Harley looking good you'll have to take care of it. However, as one poster already pointed out, it's the older Harleys of the '70's and '80's that were notorious for constantly needing work. The newer ones are much better. Just wash it regularly and follow the maintenance schedule.
Are they sensitive? In terms of potential for damage, they're no more sensitive than any other bike on the road. In terms of handling and acceleration, they're definitely more sluggish than crotch-rockets and can be more sluggish than cruisers made by other manufacturers.
TIP: Unless you really know what you're doing, you shouldn't work on any motorcycle. People who try to do work on their own bikes with basic mechanical skills usually do more harm than good and end up taking it to a mechanic or dealership to get it fixed.