It seems like Abraham gave to Melchizedek as an act of respect because he was a king.
Hebrews 7:1-2
1For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him; 2To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace;
I have a problem with the vocabulary "tithe" because pastors often appeal to the authority of old testament verses commanding to tithe. By using that kind of language they can, and often do, coerce congregations into believing they are required to give a percentage of their income to the congregation.
What I do fully support is giving or donating. It's better if we just call it giving and yes I agree mature and wise believers do give and donate.
And in Abraham's example we know that all of Levi tithed to Melchizedek. So it was more than respect. It showed that the order of Melchizedek, of which Christ is the High Priest forever, was greater than the order of Levi: the greater blesses the lesser and the lesser tithes to the greater.
I agree about pastors. They don't understand the tithe. The Levitical function of the tithe was to support the priesthood. This is what they teach the congregation so that the people give money. The Melchizedek function of the tithe is a declaration of a son of God: we get our provision from Him and not by our own hand. As a son, our provision is still guaranteed: we do not give to get. However, the tithe is one way our soul comes under the rule of the spirit. As I wrote earlier: I tithe to the man who watches over my soul. He is my actual pastor and spiritual father: much in the same way Paul was Timothy's (and others') father in the faith, and in the same way Abraham tithed to the one who blessed him.