This is pretty representative of a large portion of the feelings against Corso. Most people either love him or hate him it seems. I personally love him because he is the classic Southern gentleman, and as I from Texas, he reminds me of many of my best friends.
Those who love him recognize that he is chivalrous, loyal, and caring. He has a strong attachment to the Captain and the crew, since they are his family. He is epitomized by the phrase "I hope you don't mind if I come along and take a few hits for you."
Those who hate him see him as a representation of a "backwards" ideal where the woman needs to be rescued because she "can't do it herself." In reality, he isn't "backwards" as much as he is respectful. Just like my Southern upbringing dictates, his code of honor means he puts his life on the line for anyone, but especially women and children, who typically aren't trained in combat. The female smuggler is obviously different, as are many kick-butt women in the universe, but he was born on a small, war-torn planet where even surviving is a challenge, so some need protecting more than others. Plus, as many Southern women in my life that I wouldn't dare cross often say, "a Southern girl is a girl who knows that she can open a door for herself but prefers for the gentleman to do it because it demonstrates a sense of respect." He probably has grown up with people with similar traditions.
All that to say, chivalry isn't backwards, it is respect towards all, and especially towards loved ones or those held in high esteem, i.e. women.
They also think he is pushy and jealous, forgetting that since he lost his family, he is afraid of getting hurt again in the same way. Basic psychology.
These are just some of the reasons I love Corso. He is refreshing and sweet. The jealous bits are kinda cute at times, I haven't played my smuggler that much, but every time Corso makes a jealous comment, I giggle.