Most people who fight for 'equal rights' do it because they, or people close to them, are members of the group being discriminated against. They fight - and this is tremendously cynical, I know, but probably accurate - they fight not for an end to discrimination as a concept, or for equal rights for everyone, but to gain the privilege for their group that other groups already possess.
The civil rights movement of the 1960s was not about equal rights for everyone, black or white, male or female, gay, straight, or transgender - it was about giving straight black males the same privilege that straight white males possessed. And those straight black males (in, for example, black Christian churches) strongly fight against gay marriage, and are irritated by attempts to compare gay rights to the struggle for black civil rights, because they see, in the elevation of gay men and women from their underprivileged position, a threat to the privilege they have gained for themselves.Cynical, yes, but I think true-- well, except that I think he's overstating the last part. I don't think black men need be guarding privilege to be against elevating gays or women. They just need to not care. If it's true that most people everywhere don't care about equal rights unless it directly affects them personally or those they love, that's enough. It allows for a kind of tacit, rather than active, bigotry...the kind practiced by people who "don't care" about gay marriage because they haven't been slapped in the face by the lack of privilege confronted by gays. Fighting to protect a privilege requires awareness of that privilege, and one of the trademark qualities of privilege is that people aren't aware of it. Because they don't have to be.
I'm not going to really comment on the "As an athlete Kobe Bryant has a responsibility to be a good role model for the kids" thing. So far as I'm concerned professional sports amounts to paying a bunch of muscle-heads millions of dollars a year to wage a regular facsimile of tribal warfare. Then we are surprised and outraged every time when, instead of being models of decency for children, they engage in leisure-time activities such as dog-fighting, beating/raping women, and casual bigotry.