you should not do: turn this into a pissing contest about who has suffered more. Or a pissing contest about who has struggled harder or been braver. The comparison is and has always been about the fact that both groups are struggling to gain civil rights. Comparison to the black civil rights movement is not going to somehow cheapen, lessen or erase the black civil rights movement. The LGBT fight has had more than its share of tragedies and martyrs and heroes. It doesn't need to steal from blacks to gain respect. But it does need to make those on the fence change their perspective of what a gay person is.
This is WHY the comparison is being made. Because it helps people see gays as an oppressed group robbed of civil rights not--as homophobes would have it--a group of people having deviant sex who are demanding special treatment. If, for example, one compares the laws against gay marriage to past laws against black/white marriage, the view changes from "we can't let men have sex with men!" to "we're not letting people marry the one they love." Two men who love each other both have penises and that is not something they can easily change--nor should be asked to change if they want to marry. This is better understood if one points out the black/white couple in the past who couldn't change color and legally marry.
If you like, you can bemoan the fact that the black civil rights movement is the most potent example in the U.S. of civil rights wrongly denied--certainly the LGBT movement could as easily compare themselves to women's right or equal rights denied to certain religious minorities. But if one is trying to get people--including homophobic blacks--to understand that this is about civil rights, about people being seen for the content of their character, not for how they have sex, then comparisons to the black civil rights is the quickest and clearest way to do it. And NOT wrong. They are comparable.
The black civil rights movement is best remembered, and best understood by Americans. That's why it is used as a comparison. It's not, as you imply, because of any attempt to steal anything away from blacks.
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