I was taught the same way your professor thinks. And the E&E for Torts agrees.
"Intent" alone is not the element of intentional battery. The element is "intent to cause harmful or offensive contact, or an imminent apprehension of such a contact."
So unless the contact is intended to be harmful or offensive, as determined by the reasonable person standard, not the victim's subjective opinion, it's not likely to be considered battery. Grabbing a woman's arm helping her on the bus probably wouldn't be battery, as a reasonable person wouldn't think there was an intention to cause harm inspite of the result. Grabbing a woman's butt in a line would be even if she weren't hurt, as it's likely to be considered offensive by a reasonable person even if it didn't hurt.
This question is a total bait question that would be argued on both sides on an exam. There is no clear cut answer to this...it lies in the gray area of intent and that's why he asked it, because its a *** to answer.
Page 1 in Gilbert's Torts, Under the "Chapter Approach" heading [$$1-2] it says, and I quote..."Remember to apply the term "intent" to the result that occured, NOT the act the defendant engaged in; the defendant must have desired that a particular result occur or have been substaintially certain that such a result would occur."
Then on page 4 it says "to make out a case for battery, the plaintiff must show that the defendant's intentional act resulted in the infliction of a harmful or offensive touching..."
Talking about confusing....
Thus it all depends on which side convinces the jury over a 51% level of reasonable doubt.
Defense would argue the man was just being helpful and couldn't forsee her arm breaking, and possibly that he even had implied consent
Prosecution would argue that in order to break someones arm the contact must have been substantial and that when the D grabbed the arm he had to be certain such a grabbin could result in a break.
In the end the law usually favors the innocent and injured Plaintiff over a defendant even if he had good intentions....because someone has to be accountable and it can't be the person who didn't act.