Why did the charedi man cross the street?

Because the woman was on his side.

According to YNet,

A group of ultra-Orthodox men took to the streets of the haredi neighborhoods in Jerusalem last Friday [the 7th- MS] and called on the public to adhere to a complete separation between men and women in certain areas of the city.

The activists toured the streets near Geula neighborhood in taxicabs and announced, using megaphones that on some streets men and women should walk on opposite sides of the road during the weekend.

According to a resident of the neighborhood, Avraham Cohen, those responsible for the initiative belong to the extremist Neturei Karta stream. "The leading rabbis of the ultra-Orthodox public do not support this initiative," he said. "This group decided to on their won accord go into the neighborhoods and set new modesty codes."

However, eyewitnesses said that although the segregation had not been sanctioned by prominent spiritual authorities, most passersby heeded the call last Saturday. "During the noon hours when women go out for a stroll and the men go to the synagogue, men and women walked on different sidewalks," one resident said.

It is an interesting illustration of the way chumras - stringencies - get adopted even when no one really wants them, purely because of social pressure. It is only a matter of time before this becomes the norm.

Incidentally, in 2004, the Vishnitz Chasidim in Bnei Brak asked men and women to walk on opposite sides of the Admor Mevishna Street - it would be interesting to know whether this is still the case.