One can use both, teach or give classes.
Maybe he´s afraid of using the word "give", so you don´t think you may think he won´t charge for them!
Susan Miller, astrologer to the stars: 'April's so scary I'm giving classes on it'
Source: The Guardian
BBC News - Hothousing their way to the topwww.bbc.co.uk/news/business-14475926
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11/08/2011 - By Mark Dummett BBC News, Kota, India ... He started out giving classes in a garage, and now his school has 18,000 students.
Earlier this year ...
B dropped from school class name - BBC News