Outlook and Apple Mail are two of the major email programs out there that I see people using. Here's a couple reasons you should avoid using them.

1. Security - They are inherently a security risk. You email is stored openly. Your password is saved. Even if you change your password, those emails still sit there for prying eyes to see. If your computer is stolen, this becomes even more of a risk. There's also more data going over the network that a hacker could listen in on.
2. Inefficiency  - Using a mail program to check mail is like waiting inside your house for the mailman, waiting for him to put the mail in, then going out and getting it. Using webmail is like having the mailman hand you your mail. You take an unnecessary connection out of the equation, thus reducing risks and increasing the efficiency. The web interface is so powerful, and it's always running even when you're not on it. Meaning rules can always keep your inbox clean whether you have your computer on or not.
3. They're more trouble than they're worth - From an IT standpoint, they cause more problems than they're worth due to the tons of options that can be inadvertently changed, the local storage aspect (since it caches mail locally), the chance of misconfiguration, the fact you're paying to keep them up to date and the overall number or requests the systems normally cause.