| Quote #1
They argued with the men over philosophical, sociological and artistic matters, they were just as good as the men themselves: only better, since they were women. (1.11)
It's hard to tell if D. H. is being serious about this (we're going to guess not). He probably means the exact opposite—that women shouldn't be arguing about philosophical, sociological, and artistic matters. Instead, they should probably be bringing the men some sammiches.
| Quote #2
She was too feminine to be quite smart. (2.37)
This passage seems to confirm that Lawrence doesn't think too highly of women's intellectual abilities, but this is actually a British use of the word "smart" to mean "cool" or "fashionable." In the 1920s, all the cool girls were skinny and flat-chested, but Connie has curves.
| Quote #3
"A woman wants you to like her and talk to her, and at the same time love her and desire her; and it seems to me the two things are mutually exclusive." (6.9)
Tommy Dukes doesn't believe in companionate marriage (the idea that you can be friends with the person you marry). Connie calls him her "oracle" (6.1) about men and women—so does Lady Chatterley's Lover agree? Does Mellors?