Found here (p. 15):
According to Chazal it is forbidden to walk behind a woman because it could lead to inappropriate thoughts. Generally, on the streets today it is impossible for a man to avoid this and one can therefore be lenient. Nonetheless, a person should be careful what he looks at when walking and it is still proper to avoid walking behind a woman when possible. Since it is considered derech eretz in America to open the door for a woman and let her go first, it is recommended to do so when dating.
Footnote (105):
Rav Schachter (oral communication) said that since it is considered derech eretz in America to let a woman go first, one should do so. Similarly, Rav Willig (oral communication) thought that strictly speaking we follow those who permit walking in the street behind a woman and when possible should one avoid it. However, on dates, since it is considered polite and considerate to let a woman go first, one should do that and not be strict.
How is this a “minhag”? Goyim simply want to look at women!