Search Results: single vs. being in a relationship

I might get some backlash for this one and that's ok but I'm curious what a lot of you guys think about this conundrum. I understand that the acts themselves come from being respectful and protective of women, but if a woman herself were to request that you cut back on some of those behaviors would you?

For example:

Say you went on a day long date with someone around town and they insisted on opening the car door for you or holding doors open for you every single time. Assuming she was respectful enough to appreciate the initial gesture but asks that you relax a bit on it or even goes as far as to say it makes her uncomfortable that you insist on it so often, how would you react?

Now clearly two people who would continue to butt heads on this probably wouldn't mesh well in a relationship so we don't need to get into the long term ramifications. Again, I'm just curious to hear how you personally would react. And if you want to go a step further, was there ever a time (s) where you were trying to be chivalrous and it completely backfired on you?

Basically, in order for relationships and I guess society to improve, should men improve first, or should women?

And now here's the long explanation.
It's no secret that the divorce rate has increased in the past decades. It's also no secret that single parenthood - especially single motherhood- households have increased substantially. We are now seeing its (detrimental) affects on kids and society - higher rates of depression, aggression, suicide, poor grades and disciplinary issues, dropping out of school, unemployment, poverty, drug and substance usage and addiction, promiscuity, teen pregnancy, criminal behavior and incarceration, etc.

We see constantly people asking why relationships are failing, where society is heading as the nuclear family is being worn away if we continue this trend. Women wonder where are all the good men? Men wonder, especially in the west, are there much "marriage" material women left? How to attract such mates? I've heard many women say what's the point of being a good woman if they still get cheated on. And I've heard men say what's the point of being a good man if women aren't attracted to good men.
Common advice is you need to be a good woman to attract a good man, and vice versa. But in society, which gender needs to improve first. It's kind of a chicken vs egg, which comes first?

TLDR: So my question is, in order for relationships to be fixed in society (reduce divorce rate, reduce single parenthood, etc), who needs to improve first? Men? Women? Both? Neither? What is a "good man/woman"?
Please no trolls, misogyny or misandry.