The Islamists decry the American and European Westernized secularism because as far Islam is concerned that secular culture dishonors its women.
It is not really Islam that feels this way so much as the feelings of the proto-Islamic tribal cultures that pre-dated the rise of Islam, the tribes Islam incorporated into its culture. In any case, the Islamic world is concerned with the same ferocity about the promiscuity of the woman as it is concerned about the humiliation of the man, both of which it reads as dishonorable.
It is ironic that Western society deems Islam’s treatment of women as dishonorable conduct, not of the woman but of the men who oppress them. Western society also blames the Islamic men for the sense of humiliation, for their unwillingness to work their way out of their humiliation.