I am Lananaroux or Person A in this situation. Tyler James Young is correct as to what I meant by "Let me have it."
In my comment, I conceded that Southerners really do deal with quite a lot in terms of weather and surviving nature and the elements. However, I intended to imply that feeling like I'm hardier than Southerners during the winter months helps me feel strong enough to endure our long, cold winters. When I said "Let me have it" I meant: "Please just let me think that I am stronger for living here, where it is cold, than if I moved south, where it is warm, because whether or not it is true, the thought helps me through the winter."
I'd rather not be burdened with the truth of the matter, I would rather just have my feeling of superiority whether or not it is actually valid.
They have similar definitions, but we tend to use them to mean somewhat different things, and in different situations.
I don't have evidence for this, but as a native speaker, my sense is that we more often use abrasive to describe how a person is perceived by others, and to describe a relatively stable personality characteristic.
Many people dislike her. She often comes across as arrogant and abrasive.
On the other hand, we more often use insulting to describe something in particular that someone says or does. And more often to describe how a person is behaving or behaved in a certain instance.
The way the waiter talked to us last night was insulting.
More likely: She's an abrasive person.
Less likely: She's an insulting person.
In the context you describe, my sense is that most people would use a more casual and simple term:
Don't be rude.
Don't be a jerk/ass/asshole/dick.
A bit more formal: Don't provoke him.
Abrasive is a more formal term, and more likely to be used in writing or by someone who often uses "higher vocabulary" words.
Best Answer
In this case, it's figurative. Rounding the bases in a literal sense would be to touch the bases in a game of baseball. However, in a figurative sense, the bases represent different levels of intimacy with a romantic partner. For some idea of what they are, here's an excerpt from Wikipedia, Baseball metaphors for sex,
So, she knew that she would not win the man because she withheld sexual intimacy from him. Ultimately, I think she's suggesting that she lost because she wouldn't let him have sex with her ("home run", "scoring"). This is often considered a significant reason to end a relationship.