Yes, your instructor is correct . . . tropical names alternate male/female/male, etc. through the list each year.
Now, while Katrina and Rita seemed like "back-to-back" storms for us in Louisiana, they were separated by about a month. So there were several storms between those two storms ... here's the list from Katrina to Rita during 2005:
. . . among one of the "busiest" Septembers ever in terms of the number of named storms, and remember that 2005 was by far the "busiest" hurricane season ever. So the names did alternate "boy/girl," etc. between KATRINA and RITA . . . there were just many storms over that 4-week period.
Hope this helps!
WAFB Storm Team