how to prove objectively that despite physical, anatomical,physiological and psychological differences between men and women that everything should be the same , there must be gender equality between them
Gender equality is not a matter of proof but a matter of principle. The first book on logic that I ever read- I was about 16 at the time- had a strong influence on my subsequent development. One of the examples used by the author to illustrate arguments at cross purpose was an imagined discussion between two friends, one of whom was pushing the view that all mean are created equal, while the other disagreed, insisting that there are all kinds of inequalities, in height, weight, strength etc. The author of the book pointed out that the argument was going nowhere because the two friends were using the word equal in two different ways without realising it. You seem to be making the same mistake in your question. When we talk of gender equality, we don't mean that people of different genders are identical, but that they should have equality of rights etc.