As Vs Like: Correct and Incorrect usages

Hi Payal,
Please guide me on the below question.

Teachers in this country have generally been trained either to approach mathematics like a creative activity or that they should force students to memorize rules and principles without truly understanding how to apply them.

a) to approach mathematics like a creative activity or that they should force students to memorize rules and principles

b) to approach mathematics like a creative activity or to force students to memorize rules and principles

c) to approach mathematics as a creative activity or to force students to memorize rules and principles

d)that they should approach mathematics as a creative activity or to force students to memorize rules and principles

e)that they should approach mathematics like a creative activity or that they should force students to memorize rules and principles

I think here we are trying to compare "mathematics" with "creative ability"(do not think here "as" can be used as a function) , hence 2 nouns are being compared. I opted for B but the correct answer is C.
Please help me understand whats wrong in my thinking.