It is very complicated. You have to read the Cochrane review and understand the statistics.
Mammograms work better as a screening tool the older you are and the more at risk you are (usually strong family risk).
Otherwise, what they find might go away on its own or not come to anything but you would get investigated, biopsied, surgery, radio/chemo therapy and drugs that may contribute to your future demise or reduce your quality of life in a way that is not accountable in the statistics. Screening by mammogram does not result in the drop in the number of deaths that you would expect. It is impossible to quantify this accurately, and impossible to know which abnormalities will cause someone to die, so if you have the mammogram and it finds something, you just get treated. Some people prefer not to have the mammogram in the first place.
At the moment, the National Screening Committee feels that the benefits outweigh the risks for the general population.