A word or expression for "behaving badly because he wants her to hate him”

He's pushing her away. That's the most classic/commonly used phrase I can think of to describe that situation.

You could say his behaviour is sacrificial,

[To] sacrifice: 2. give up (something valued) for the sake of other considerations.

Or it is self-deprivation,

Voluntary denial or suppression of one's own interests or desires.

If you want to portray him in a good light, you'd say he was selfless:

Concerned more with the needs and wishes of others than with one's own; unselfish.

He probably thinks he is behaving for the greater good, which is to say

a general advantage that you can only gain by losing or harming something that is considered less important

incite

Incite suggests provoking emotion that would not otherwise be felt, and action that would not otherwise be taken.

tr.v. in·cit·ed, in·cit·ing, in·cites

To provoke and urge on: troublemakers who incite riots; inciting workers to strike. See

Synonyms at provoke. [Middle English encyten, from Old French enciter,

from Latin incitāre, to urge forward : in-, intensive pref.; see IN-2

• citāre, to stimulate, frequentative of ciēre, to put in motion; see keiə- in the Appendix of Indo-European roots.] in·citement n. in·citer n. The American Heritage® Dictionary of the English

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