As far as I know, you can only send emails via a third party client (i.e Apple Mail, Thunderbird, Entourage, etc...) if you upgrade your account to Yahoo Mail Plus as we had the same problem a year or so ago.
Yahoo Plus is $11.00 per year - is it worth it? er...no. Trying to persuade my wife to go to Gmail, but alas the lady is not for turning...so, get your Visa card out and then pop in these settings into Mail:
Incoming Mail (POP3) Server: plus.pop.mail.yahoo.com (Use SSL, port: 995)
Outgoing Mail (SMTP) Server: plus.smtp.mail.yahoo.com (Use SSL, port: 465, use authentication)
Account Name/Login Name: Your Yahoo! Mail ID (your email address without the "@yahoo.com")
Email Address: Your Yahoo! Mail address (e.g., user@yahoo.com)
Password: Your Yahoo! Mail password
This, theoretically, should work. However, we are having some major issues with Yahoo Mail at the moment even though we are using Mail Plus - can recieve but cannot send...sometimes. Why? No idea.