No, man and women friendships do exist without ulterior motives. I am one of them. Two of my best friends are guys. We became good friends since junior high. Nothing has ever existed apart from the wonderful friendship we have. One of them is married and the other one is about to get engaged - both are straight. The one that has a kid already even calls me aunt. Both of their partners even feel comfortable around me because they know that we treat each other as friends, basically like siblings and nothing else. I even go out places with the girlfriend of the one that’s about to get engaged. It’s not common but women/man friendships do exist.
Then by your logic, I would be lovers with my male friends already... That thought is so tiring... Funnily enough, I never had a boyfriend in my life.
Actually relationships between different genders can totally exist, romance and sexual free! My bf and I are part of a pretty large friend group and it’s a melting pot of people. People who are single, in relationships, guys, girls, and everything in between and outside of that. I have many guy friends and my bf has many friends who are women. Friendships like that are very valuable. You can get the perspectives of the opposite gender if you ever need it which is just another plus. It saddens me to know how many people are losing out on possibly the best friendships of their lives because they feel as if people of different genders can’t genuinely be friends without hidden intentions or the “guarantee” of it growing into something more.
"a man and woman can't stay friends" well I totally agree with u unless one of them is gay or both ... Heh simple ¯_(ツ)_/¯