Possibly because Mother's day has religious connections (certainly dating back several centuries), originally as a feast honoring Mary but later expanded to all mothers.
Father's day is a 20th century invention created to mirror Mother's day. Though it has precedants in the early 20th C., it didn't become an official holiday in the US in 1972!
CDH.
I think you are overemphasizing the religious aspect as to why Mother's Day is "more popular." It was begun by Ann Jarvis, as a movement to rally women to improve sanitation in the 1850's, then to specifically improve sanitation in camps of both armies in the Civil War, and then to re-unite the country through mothers after the war. It quickly became a hugely commercial holiday, and Jarvis became one of the day's biggest critics because of that.
IMO the answer has been given in some of the posts in this thread. Mother's play the guilt game better to emphasize the day, and father's aren't supposed to care about that sentimental crap.
What I notice is that more people come to church with mom on Mother's Day, where at least in some congregations having the most of your kids with you is a big status point, and more people go fishing, or to a ball game, or anything other than church, on Father's Day.