I wouldn’t pay that English teacher no never mind. Lots of things “sound right” to lots of people.
The “string” in “hamstring” is not derived from the verb “to string.” It is the name of a part of the body. Thus, the verb “to hamstring” is analogous to “to gut” or “to skin.”
A person who hamstrings is not doing any stringing of anything—he is cutting. I.e., cutting a hamstring.
1 : to make ineffective or powerless : cripple <hamstrung by guilt>
2 : to cripple by cutting the leg tendons