If you’re unable to transfer Pokemon to the Professor after the update today, it’s because the transfer button has been moved. I think they must have moved it because when you scrolled to the bottom of the screen (which was a pain to do), the old transfer button was underneath the X button to close the window.
Now, to transfer Pokemon to the professor, click on the Pokemon (as you would before they removed the transfer button) then click on the button at the bottom right. The button should look like a list menu button (3 horizontal lines, or the Chinese symbol for the number 3). From here you will then be given the option to either mark the Pokemon as a favourite or transfer it to the Professor. Click the transfer button to transfer it to the professor.