There's a difference between being buddies and crushing on each other
Yeah, this seems obvious. But it's not always, and nowhere is that murkiness greater than in the brain of the person who keeps calling that guy who's clearly in love with her, her "brother." Yes: mature, rational people should be able to tell when their friends want more than friendships. But it's just not always that easy… so don't automatically assume she's doing anything inappropriate.
If you find yourself in this situation, your best bet is to try making him your friend, too. If he resists, you've got a good case to present to your girlfriend. And if he complies, you can have a man-date (or several) and gain a bunch of insights about him. Maybe you'll even discover he's not such a threat.
What you want to avoid having is a jealous fit in front of your girlfriend. It will make her act defensive, paint you as a crazy person, and make her best buddy suddenly seem like a way more viable option.
If this "brother" figure is rude to you, he's not really her friend
General rule of social etiquette: be polite. To everyone -- and most especially the man or woman your friend has chosen to be with. Sure, you're not going to love them all; but you can still act like a reasonably decent human being so long as there isn't abuse (physical or emotional) or fraud (cheating) going on.
If you're dating someone who refers to that guy who's rude and obnoxious to you as "like a brother," it's fair to ask why someone so close to her would be so shitty to the guy she's with. If there's no clear reason for the behavior, sorry to say but there's often jealousy involved. And a reliable, healthy, loving partner isn't going to surround herself with people who unjustifiably disapprove of the relationship.
If you're newly coupled, it's time to focus (on each other)
It should be understood that a new couple starting out has one very important, burgeoning relationship to invest time in… and it's not the one between two friends. You can’t possibly learn the ins and outs of a person if her “brother” is consistently in and out of her: on her phone, in her texts, at every function she is at, or, possibly literally, in and out of her.
By no means am I saying to dump a woman just because you noticed she has a lot of guy friends. Nor should you stop trusting her. BUT! If she’s texting the smirking-I’m-not-wearing-any-panties emojis, giggling at comments that don’t even warrant laughter, and play-fighting with her "brother," it's fair to say something is amiss. And yeah, at that point maybe your guard should go up.