Why are most older brothers kinder and more generous and nicer in general to younger sisters opposed to younger brothers?

They aren't.

At least half of the time, I mean my older brother is a gross, immature, patronizing, sexist pig. He's not kind to me at all. See what I mean? A lot of younger (and older) sisters will tell you this. It depends on the relationship between the siblings. I mean, if the two are friends, then they probably will have a good attitude, and maybe the brother will feel obliged to be nice to her. Also this works if there is an age difference, especially a big one. Also, if one of the siblings is really unkind, then that will affect the relationship too.