Bob already presented some of the most basic reasons why.
I'll just add that while it's good you're taking an active interest in computer security... Your average newspaper is hardly a reliable source for a complex technical issue such as computer security. Even tech oriented sites like Cnet, are rarely reliable sources for such information.
I'm sure the author of the article meant well, probably checked a number of facts, but also likely had little more than a layman's understanding of a broad and highly complex subject. As a result, some things were probably misrepresented. There's also the distinct possibility that the article was factually correct, but you misinterpreted something.
So, here are some basic tips to keeping your system problem free for long periods of time.
1: Do not use Internet Explorer, or anything based on Internet Explorer. Replace it with your choice of Mozilla Firefox or Opera
2: Be sure to always apply security updates issued by Microsoft and the makers of any other programs you use. This is the only valid exception to rule #1.
3: Avoid all file sharing, or P2P, programs
4: Avoid all pirated programs
5: Be sure to have a virus scanner installed (AVG Free and Avast are free for home use if you're cheap or poor)
6: Have some sort of firewall running. XP/Vista's built in firewall is good enough, otherwise there are third party products like Zone Alarm which have free versions if you're not running XP/Vista
A few others, which have less to do with security, and more to do with just making life on the Internet a bit more enjoyable
7: Do not use Outlook or Outlook Express for email
8: Do not open ANY attachments in email messages, regardless of who they appear to be from, without scanning them first with a virus scanner. Do not rely on automated scans that are supposed to happen as the message is downloaded. It also never hurts to fire off a quick message asking the person to confirm sending you the attachment
9: Never respond to any spam messages that claim to offer a means to remove you from their mailing list
10: If you get a message claiming to need sensitive information, or offering some sort of too good to be true deal, it's probably some kind of scam
11: Never click on a link in an email message, always copy and paste the link into the web browser manually to avoid specially crafted links designed to trick you
12: Never trust anything sourcing the website grc.com as reliable
13: Create a free account with a service such as Hotmail or Yahoo to use for signing up for website services, so when they spam you with newsletters and paid advertisements, they don't clutter your primary inbox
14: Be very selective about whom you give your real email address to in an effort to reduce the amount of spam you receive. Do not be afraid to set up several accounts like from #13 for different purposes
Others may have additional suggestions... The first 6 are the ones that you should consider mandatory if you are serious about computer security. All the others, 7-14, are optional, but good ideas to follow.