Women rarely approach men if at all. The "too fat, old or too whatever" are usually too self concius and rarely do it if there is not an indication of interest. In fact men complain about women not approaching at all. Make up your mind, should women approach men (and then you would have to accept that women that they don't like do so) or not?
Women have already say that they don't want strangers approaching on the streets. They complain about catcalls and being approached on the streets. So it is not a double standard, it is just women not liking being approached and preffering to only get flirting at places like dating apps or pubs or places where people go to meet people. It is not rocket science. Young people have been introduced by common friends for a long time. It is not as if there is no ways to meet people without being approached.
And with dating apps, introductions and other ways to meet people, you'll avoid the most common reason of rejection: having already a partner. So when you say "rules for thee, but not for me!" to which women are you refering to? I mean, do they really exist women that approach men on the streets?