The primary reason your comparison fails to hold water is that you are mixing two different arguments. One (the civil rights movement) was claiming equality on matters where it actually exists, namely an equality of human dignity. Blacks were being deprived of certain things based on nothing more than skin color. Obviously, that is absurd.
You are trying to take that argument and use it in this case, which is a discussion of something entirely different. If we were claiming that women were sub-human or some such nonsense, your argument would have merit, but we are claiming no such thing. Just because two people possess an equality in human dignity does not mean that they serve the same role in society, or that they should be doing all of the same things. There are differences between the sexes that go far beyond the physiological. They are wired differently, have different strengths and weakness, and as such, are complimentary. Each has a particular and distinct dignity. In fact, it is precisely due to the dignity of the female sex that I am opposed to them wrestling. It is not a matter of depriving them of something they have an equal right to. It is a matter of protecting their dignity, even in cases where they have chosen to forego that themselves., and protecting our sons from a gradually (or not so gradually) eroding view of women.