Hopefully all the spellings are correct…
I just started watching Criminal Minds for the first time - if not entirely in the right order, close enough enuf for government work. 
why does this strauss person so thoroughly want to destroy the thomas gibson character??
From what I recall, Hotchner was initially portrayed as very ambitious. He wanted to be head of the FBI someday. I think she viewed him as a rival in terms of promotions, and that sort of thing. Working for the BAU is very prestigious, so she wanted him out of there, so she could assume control.
I think.
Strauss appeared in the middle of things, certainly after Mandy Pantkin left, if memory serves. And if further memory serves, the Strauss/Hotchner thing started when the Reaper serial killer targeted Hotchner’s family.
There was also tension with the team at large because Morgan refused to take Hotchner’s job permanently when Hotch took time off after the Reaper case.
I’m also thinking maybe Hotchner might have been offered a promotion and he refused? (Sort of like Riker on Star Trek, he could be a bigger-wig at the FBI but he’s “too committed” to his current job.) Hoping to bump this in the hope that someone with a better memory comes along…