It's not about Floyd as a person, it never was. It's about what his death represents. That a police officer looks right at the camera as he kneels on Floyd's neck, hand in pocket, casually extinguishing his life is a powerful statement, not about the individual, but about the system. The people who killed the 77 year old black man weren't acting with the authority of the state, but those responsible for Floyd's death absolutely were. To view this outside of it's social and historical context misses the point, actions such as those of Chauvin and the other officers in Minnesota are visited on black men far more often than white men. The evidence supporting this is readily available, one can choose to accept it as legitimate, or not. There is debate as to why it happens, with divisions largely along the lines of political ideology, but that is a separate conversation.
Application of Constitutional rights in this country should not be dependant on how good or nice a person is, what color their skin is, how old they are, which god they do or do not worship, who they love, what their hobbies are, where they live, what they drive, etc. Life and liberty are two fundamental rights which are guaranteed by the Constitution, and through practice are not applied equally across racial lines. Thus, black folk have been crying out for the equal treatment promised by the Constitution since 1865, but still it remains elusive.
Using terms like "your race" and "our race" implies fundamental differences between groups for which there is no biological basis, and allows a foundation for racial stratification. With stratification comes unequal distribution of resources, and when these resources are the means by which people have the ability to improve their lives, systemic disadvantage follows. As I've said to you on previous occasions, any way you want to look at who is advantaged in this country, the scales tip in favor of white folks. It's incredibly frustrating for people who are acutely aware of their being on the short end to be informed that not only is that not the case, but that they are disrespectful or ungrateful for pointing it out. If white privilege doesn't exist, why do people work so effing hard to hold on to it? Privilege of any type isn't something to be ashamed of, you didn't ask for it, but for crying out loud, if you're not going to use it to enact meaningful change, at least acknowledge that it exists. Everyone in the entire world recognizes that white folk in America have privilege, with the exception of some white Americans. Those folk will go through some pretty incredible mental gymnastics to keep trying to deny what everyone else plainly sees, it can get rather comical.
Regarding your question about heroes in the black community, when people are made aware of the significance of their racial differences, and all they are taught about in their formal education is white American heroes, whilst constantly being bombarded with negative images of people who look like them, does it honestly surprise you that many black kids pick some really poor examples to look up to? Not coincidentally many of the"heroes" all kids are taught about in school were not good people, history just overlooks their shortcomings. Many of the founding fathers owned slaves for example, and that's glossed over as just the way things were. As if there could be justification for owning another human being as property.
You use the term commonly shared ideals, while implying earlier in your post that black and white ideals are different, and that's interesting. Do you think that black parents teach their kids different values? Have different morals? Desire different outcomes? If so, is that because they're black?