Knowing nothing about you and your mom's relationship, I would ask yourself if she's a good judge of character on this particular issue. You only met him 2 weeks ago and were pretty hasty to bring him to the house, so maybe it is seen as jumping the gun (or been seen that way)... and if he was actually "cocky" with such a short relationship, maybe the relationship has gone to his head quite a bit for such a short period and she may see it as a red flag
Mothers are protective of their kids, but maybe consider with how short the relationship is, him being cocky may not have been OK for someone she (and you) barely know in this way. Some people really value their family's opinion, to the extent they will break up with folk... others, they don't have that kind of family anyway. So consider where her opinion matters for you.
I almost always think it is worth an argument to speak with someone I care about about issues between
us. The exception is when the person is already well aware of the conflict they are causing or if there are emotional problems that cause them to act a certain way...
The other possibility. If you've had a string of bad relationships, then your mother may be overly protective and erring on the side of viligence. It's stressful to see someone we care about get hurt over and over again... and if he's cocky, and she's seen you've been majorly mistreated, then she may be drawing boundaries where
she can in order thinking hopefully you'll get the message... after all, if you're old enough she can't tell you what to do, then this may be her way of not only warning off the bf but you for who you bring home... (again knowing
nothing about your history) ...
If you really feel it will risk a major argument, then consider that there is more going on with her opinion than just the bf... if she is just this opinionated in general, then obviously the context would be very different... some people are just judgemental, but because of how blunt she was, maybe he did something that she felt went way over the line... and she is not good at putting that into words except for sounding overly critical. Sometimes that's not clear what is really felt when people are upset... you could wait until she's less upset.
If this is your mom, then I think give her the space "to be" who she is, and maybe respect her wishes... at least until until (and if) the relationship is far more serious... maybe also give it more time before bringing someone home, that way you have more experience with that person, you can use that to explain some of their behavior if your mom is a nit-picker... again, all depends on context and a ton of variables
... it could just be that they're oil & water... it happens.