Could the X-rays women are exposed to and the compression during mammograms be an environmental element that could contribute to women getting breast

It depends on the age of the person getting the mammogram and the amount of exposure involved. Unfortunately, younger women are at a higher risk from radiation than are older women. We know this because of the data developed from Hiroshima where young girls and women under the age of 20 who were exposed to radiation had a much higher risk of breast cancer when they reached middle age. But women who were already middle-aged when exposed to the radiation at Hiroshima did not show this increased risk. So diagnostic radiation from mammography in women under 40 or possibly in women before menopause in general may well carry an increased risk of cancer associated with radiation alone. We certainly know that radiation of a pregnant woman will increase the risk of leukemia in her offspring.
There are studies of children who have been irradiated for specific diseases such as Hodgkin's, who developed breast cancer later on. So there really is a childhood age range where radiation should be kept to an absolute minimum.