Could a translation error lead to squares to not be considered as rectangles? (Mandarin)
My guess is it depends if rectangle is translated as:  


  
  Oblong   
  Quadrilateral  
  


Could be the case that the teaching is for young children, where the word / concept of rectangle vs Oblong vs Quadrilateral might be difficult to understand, but it is essential for them to differentiate between square and Oblong

Others (parallelogram, trapezoid/trapezium, rhombus) does have a specific name and are not confused with rectangle.