Yahoo is pushing a new interface
"You're invited to try the best Yahoo! Mail ever."
With a big button saying "Try it now" and no button to let you decline.
The only way to read your email with Yahoo email Classic is to notice the small print "No, thanks. Continue to Yahoo! Mail Classic." link in the middle of two paragraphs of "Terms of Service" and similar material.
I have a Yahoo account where I clicked on the "Try it now" button, assuming it would be easy to switch back to Yahoo Mail Classic (I've switched back to Yahoo Mail Classic at various times in the past),
but it seems the newest Yahoo Mail interface doesn't have a way for users to switch back to Yahoo Mail Classic.