One of the nebulous issues in such debates is the concept of 'respect' as it applies.
Though some of the behaviors often shown by 'gentlemanly' types toward women are also shown toward the advanced elderly, the obviously severely handicapped and young children (all perceived as weak and needing assistance at times), such behavior is often attributed not to a low estimation of a woman's abilities, but to 'respecting' women.
Which means what, exactly? We're supposed to 'respect' everybody, unless & until given cause not to. The context often implies that women are (for whatever reason) to be shown/assigned either additional respect, or some type of respect, that men are not. Women as a general class, not just one's wife, daughter, mother...
The answer must lie in some value system, since it clearly assigns some value difference to women vs. men. Our society has tried to move away from that, though there are still entrenched remnants (e.g.: debates over women in military combat, and the old 'women & children first' cliche' show our society still views men as more expendable than women).
So while the exercise of deferential & preferential treatment may not be rooted in condescension or a presumption that one is superior, it is rooted in a sexist view on some level.
Richard.
P.S.: Elsewhere I've seen before the argument 'Well, that's how my father taught me...' I'm 40 something and I remember a bit of that generation and their common views on equality, too. Using the N word for blacks was common and (when none were around) accepted, inter-racial marriage viewed as wrong and while they didn't promote slavery, a lot of them weren't fully convinced of true equality. Not all that couple of generations believed and practiced that way, but it was common. Considering the source, I'm a tad skeptical of their wisdom in treating groups differently. I bear that in mind when a view is justified in terms of 'old fashioned' values.