Shouldn't "his secretary changes every week" be also correct?
No, because it's passive.
Yeah in Hebrew it's passive but the meaning of my English phrase is (almost) same - that there's a new secretary every week. I believe this is called middle voice in English
That has a different word in Hebrew. מתחלפת is like middle voice. It is considered big active and passive.
Here, in both languages, the secretary is not acting, but being acted upon.
How about his secretary is exchanged every week?
Exchange= give and receive in return sthg. of the same type or equal value.