I have several GMail addresses, and a Google Apps email address for work, and variously-hosted other email addresses, all managed from within Thunderbird (with several extensions found over the years).
I don't want to merge personal stuff with my work email; I don't want to merge my work email into a personal gmail account; and above all I don't want to do either of those things then find that some robot in the system has locked me out of my account.
I also really need to have full offline access, so I can work in spite of unreliable or infrequent net connections. I.e., in 20 minutes of internet access in a crowded coffeeshop, I can upload dozens of responses to yesterday's mail, and collect today's mail, and fit in a few rapid realtime messages, then go. I'm not often forced to work this way, but when I am this is a lifesaver.
No ads (and no need to try to avoid them). Nobody systematically reading all my mail to custom-tailer said ads.
Easier integration with client-side encryption tools to facilitate end-to-end encryption.
Better support for plugins and other modifications.
I'm sure others have variations on this theme.