I get along well with women and men, and I don't think women see each other as a threat.
It has been a privilege to share my life - at school, at work, at home, socially and in the community - with many, many wonderful women. Women who are smart, hard working, compassionate, funny, capable, generous, and sharing. I think that because I've been a mom my entire adult life, most of my contact with the world outside of work and family has been through the prism of motherhood, so most of the people I know well and see frequently are moms. That said, I work with mostly men and have a house full of sons, so I also interact with men (their coaches, teachers, friends' dads) on a regular basis and get along with most of them as well.
People are people. It drives me crazy to read people say things like "I don't get along with other women; they're all catty and jealous" or "I hate men they're all stupid." Such a sad, narrow way to look at the world.