This quote is an excellent example of the hypocrisy of his attitudes about women. Based on his behavior and expectationsof Myrtle, it would seem that he thinks it is just fine for a married lady to "run around." Look at how established he is in that relationship! The two of them have a furnished apartment to go to -- not some seedy motel at the end of road. He brazenly talks to Wilson, all the while, secretly planning to meet up with Myrtle later.
On the other hand, it is NOT OK for Daisy to have any kind of life outside of her marriage to Tom. He is demanding and controlling because that is the societal expectation -- especially in his social class. These people don't have public scandals, and the women know their place is in the home. He calls himself old-fashioned. He is in regards to his treatment and attitude about his wife. She is treated almost as a possession.
I think the final irony is that it is an "old fashioned" stereotype that men can run around on their spouses, but women cannot. The old attitude was (is?) "boys will be boys." On some level, women were expected to tolerate this behavior, and sometimes didn't have many viable choices, considering that they may have had little means to support themselves outside of marriage, and the social stigma of divorce would have had a more negative impact on the woman than the the man.