It is normal for men to look after women?

Yes. Maybe not as strongly and as shameless do some, but yeah - this is normal. It would be wrong to be different.
Man (male) gene is set to be attracted to females, something without which normally would not increase.
No wonder one of the first commandment given by God to man is: <God blessed them, saying, "Be fruitful, and multiply, and fill the waters in the seas, and let birds multiply on the earth.">