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Agree, this is confusing b/c the default screen doesn't show an option to switch rider.
As the commenter above notes, you have to make sure that you choose a different "From" location (not the default My Location) to choose another rider.
One other option:
In Settings you can add 'Family' which enables you to pay for other people's rides. It searches your contacts, sends that person a text, and then once they confirm you can pay for their rides.
So, if you make your friend "Family" you should be able to pay for their ride!