The word equality is an interesting word for the apostle Paul to use. The point that he is making is that there needs to be openheartedness on the part of all the churches to each other according to prevailing needs.
The Church of Rome has yet another interpretation of this verse. Ever anxious to find justification in the Bible (for which there is none) for their hierarchical system and their dominating pope and bishops, by which the individual churches and the individual supposed Christians are at the bottom of this hierarchy – the authority is all top down, from above – they take this passage and, ignoring the sense of the original grammar, they twist it to mean this: ‘That now at this time, your abundance, your money, may be a supply for their wants, that their abundance’ – and they interpret this as Rome’s authority and teaching and direction – ‘may supply your want.’ In Paul’s example it is Jerusalem not Rome, but according to the teaching of the Catholic Church it will soon be Rome. So the idea is that Jerusalem now, and later Rome, the mother church, will direct you, and give you the authority and direction, and you will give to them your substance in their need. Well of course, that would not be likeness at all. No, it is about benevolence and care: what you give to Jerusalem, they may one day need to be giving to you, the same care and benevolence and support – nothing to do with the justification of the Catholic and Episcopal systems of church government.