Because your valuable data gets locked to a company, and you may or may not be able to get it back in the future depending on how much they care, and want to give support.
Something like Thunderbird works better in two ways. First, it's cross platform. If you decide you want to run OSX or Linux, you can take your mail with you, and it'll be a familiar interface. Second, if Thunderbird ever ceases development. you can keep it going yourself by writing code, or paying someone else to. Odds are, there'll be enough people that want to do what you want, that you won't have to code, or pay anybody. The point is, the program's yours do do as you see fit. Your data won't be held hostage to the whims of a company whose main motivation is profit.
Edit:
For a little perspective, I'm probably running Linux now due to my mail being held by a proprietary Earthlink mail client. I had a hard time getting my mail back, and swore it would never happen again. That's when I started running Thunderbird. That got me thinking about all the other software I run, and I started transitioning over to free software in Windows. Free software got me interested in a free O/S, so now I'm running Linux.
Now I can't code, so a lot of the potential benefits aren't immediately accessible to me, but the /potential/ is there. I can pay to get what I want, or petition the community, and someone might like my ideas, and take the project on. Not being limited by artificial restrictions, or a company's bottom line is very liberating. It's like your parents telling you you can grow up to be president. Odds are you won't, but you always have that potential. You're free to do as you choose.