Equality
Equality is not a thing in itself. It has no metric. It can only be judged through particular processes in a system such as opportunity, allocation of resources, considerations, outcome, etc. I endorse the idea of equality of opportunities, not of outcome; and equality in pluralism, not equality by elimination of differences; and equity in allocation of resources, not equity in allocation of outcome.
Opportunity Vs Outcome
Equality of opportunity is the idea where everybody is given equal opportunity; thereafter, whoever is competent, will pass through. It is a celebration of liberty because it allows an individual to choose whatever he or she wants, respects that decision and rewards that individual if competent.
On the other hand, equality of outcome is the idea that the outcome of system must have an equal or somewhat equal representation of the diverse participants. This concept design is oppressive, disregards competence, discriminative and imprudent, as explained below.
Most do not realise that equality of outcome and equality of opportunity are contradictory. The irony is that equality of outcome is the opposite of equality of opportunity. For instance, if we allow 100 people to choose a profession, it is stupid to expect that each profession will have 50:50 man-woman ratio. People will choose what they like, which will not yield a 50:50 ratio. If you want such a ratio, you'll have to force men and women that they cannot choose whatever profession they like, they can only choose those professions where a particular gender is less. This is a form of forced employment; thus oppressive.
Equality of outcome disregards competence by valuing primarily those factors on which the outcome is judged, such as race, gender or colour. Although, within these factors, people are still selected on the basis of competence, equality of outcome disregards competence at the fundamental level because if you are to represent 5 people from set B, this system will force you to hire 5 of the most competent people from set B, not 5 of the most competent from the union of set A and B. It is possible that the most competent from set B can be most competent of set A and B, but there is no way to judge this. You can only judge competence when people competed against each other.
For the same reason, equality of outcome is discriminative. You are forced to take people from set B simple because they are from set B, and the more competent people from set A were rejected simply because they are from set A. And this discrimination is not even justifiable because the trait required was competence.
Equality of outcome is imprudent because the variables of the system is not within our control. In any system, it is best that the variables of the system is in our hands so that we have tighter control over the system. Such designs are bad and unreliable. For instance, sex of an offspring is not in our hands and yet equality of outcomes advocates to have approximately 50:50 male-female ratio. So it requires the system to interfere with nature's design to ensure an approximate 50:50 male to female birth ratio. I leave the ethics of such interferences onto the reader. In the case of gender, the intervention will be to mould children into whatever number of men and women required for the quota.
It gets worse: the political faction that implements equality of outcome is the same faction that proposes the more than two gender theory. Some of them say there are 100 genders, now forcing society to bring up children in 100 different ways to fit the gender quota. It's too unnatural; therefore a bad design.
Representation
The idea of representation is not a manifestation of opportunity but of outcome. It is a way to get accepted at the cost of competence. Let us also not confuse diversity and representation: diversity is the existence of pluralism while representation is a nonsensical perspective given to this pluralism.
We can be plural without being represented. The idea of representation roots from the same thought that gave rise to the concept of equality of outcome. Representation is an outcome, not an opportunity; therefore equality must not be judged by who is represented, but by who is denied the opportunity.
Reservations are a consequence of the idea of representation. They makes sense only where one party has an intrinsic disadvantage over the other, but not on the metric of competence. In India, we have the reservation of few seats in buses and reservation of train compartments for women. This makes sense because they are physically less stronger and less enduring than men. The rest of the seats are available to both sexes despite the reservation. Such reservations are acts of support.
Elimination
We have multiple identities: ethnic identity, statehood, nationality, racial identity and the identity of homo sapiens. Equality does not mean eliminating these identities, because for equality to technically exist, there must be differences in the lot. When everything is same, there is no need for the concept of equality. Therefore equality must not mean the elimination of diversity, but the acceptance of diversity and assertion of equal rights of every participant in the diverse pool.
Secondly, we can ever eliminate the differences in our characteristics because they are not in our power. For instance, race is an evolutionary reality on earth and you cannot eliminate these unless you commit a racial genocide. Sex is another reality and equality but you cannot eliminate the sexual difference unless you exterminate a particular sex. Gender too, is a reality which you cannot eliminate because you do not have control of 7+ billion minds of the earth.
These characteristics are not something bad to be eliminated in the first place. I do not think that being a man or woman or whatever the new genders are, are bad things to happen in our lives. So, there is no need to feel ashamed or offended when someone refers to your gender; or even race for that matter. There is no need to be neutral.
Therefore, equality should not mean the elimination of various races, their significances, strengths and weaknesses or even the mention of it. For if that is how equality is defined, we can achieve equality only through the destruction of certain races or gender. Nor must equality mean a systematic and organised cross breeding culture to create a mono-cultural population because it is impossible to create mono-culture genetically. The racial traits will still exist in a mono-cultural progeny in various generations. Moreover, a mono-cultural or mono-racial population will not have any diversity at all in practice, thus eliminating all the contributions of diversity.
Some try to be inclusive by following one culture. But inclusivity does not mean mutation to the new entity. It simply means accepting and including the new entity into the current social group and being tolerant and accepting of it without you mutating to the new entity.
There are many such idiotic and illogical definitions of equality out there, primarily because many received illogical education. Others, because of political and professional pressures, creates such definitions for their survival. We are living in a world of redefinitions. Such redefinition will alleviate the gravity of being a particular ist or phobe. It's just human nature that once you get exposed to a word or thing several times, it stops shocking you. To add to this effect, when people come to realise that he or she is being wrongly accused of, the seriousness of such accusations drops further.
I prefer to stick to the original definition. Only when an ism carry the character of indignation and a hint of false superiority, does that ism become an elimination worthy ism. Mere discrimination, segregation, classification or mention of races without any such character is not bad.
Equity
Since the logical unsoundness of equality of outcome and sociological evidences of its destructive nature, many who were fighting for it have now masqueraded it as equity. They talk about allocation of resources, opportunity or outcome in the name of equity. Well, equity isn't the allocation of these assets, it is the removal of hurdles to access these assets. In other words, equity is the allocation of smaller resources to access a bigger resource, opportunity or outcome.
For instance, if there is a post for a teacher and one citizen have no access to the social infrastructure like education to makes him eligible to apply for that post, while another citizen elsewhere have the access, equity is enabling the first citizen to have access to an educational institution where he can educate and qualify himself equally as other do for that post. Equity must not be giving him an unfair advantage in the education system or allocating the teaching post to him.
As a second example, consider the usual pictorial representation of equity is a mango tree with fruits hanging in unequal heights. One person is given a shorter ladder to pursue the low hanging mango while the other is given a taller ladder to pursue the higher hanging one. This is allocation of resources and opportunity; not the allocation of access. Equity in this case is to ensure that the shorter person has no restriction to procure enough wood to make the taller ladder.