I love the idea of Father's Day and Mother's Day. Changing the name of Father's Day is ridiculous, and is really telling of how PC our culture is becoming nowadays.
If we change Father's Day to Special Person's Day, which I sure hope we don't, then we should get rid of the name Mother's Day, too, because of 'gender equality'.
There's really no need to change the name anyway, though. In a study conducted from 2012 to 2013, in Australia, 1.9% of males and 1.2% of females identified as homosexual. So if your reason to change the name of Father's Day is because it excludes homosexual people - just remember, they make up only 3% of people. We shouldn't make changes to the way we do things based on a tiny minority. That's like saying we should bring back the death penalty in Australia - after all, 23% of Australians believe in the death penalty, and that's a lot more than the 3% of homosexual people in our country. So if we change the name of Father's Day, we might as well do everything that every minority wants us to do, right?
Also, changing the name of Father's Day devalues the importance of fathers. Fathers are an extremely important part of most people's lives. Just because a small number of people may not have a father figure in their life, does not mean we should pander to the minority. My friend doesn't have a stable father figure in her life but I don't see her complaining on Father's Day.
Yes, some people don't have a father figure in their life. But this is the minority, and we should not base big decisions that affect almost everyone on the opinions of a few.