To make your personal enemy or rival

I'm watching the GOP debate, and I'm noticing that some candidates are picking on Hillary.

Is there a verb for an act where a person castigates someone else in hopes of making that person his or her personal rival or enemy?

Solution 1:

It sounds like baiting. American Heritage Dictionary defines bait as

To entice or provoke, especially by trickery or strategy: He baited me into selling him my bike by saying how much I deserved a better one.

Solution 2:

Alienate:

to make (someone) unfriendly : to cause (someone) to stop being friendly, helpful, etc., towards you

Or similarly, estrange:

to cause someone to be no longer friendly or close to another person or group

These words typically indicate that at least a cordial relationship existed previously, but actions are taken to cause that relationship to cease.