The above verse can be refuted with the verse below:
“For if He were on earth, He would not be a priest, since there are priests who offer the gifts according to the law” Hebrews 8:4
The existing ordained priest, while Jesus was still on earth was the Levitical priest and tithing was given to them as their inheritance due to the duty ordained to them.
“And, behold, I have given the children of Levi all the tenth in Israel for an inheritance, for their service which they serve, even the service of the tabernacle of the congregation” Numbers 18:21
This is according to the law and, what did Jesus say?
“Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil” Matthew 5:17
He did not come to destroy it but fulfill it, He respected the law while it’s not yet fulfilled, the existing priests (Levitical) were still allowed to function and since they still function, what the law says about what needs to be given to them still applies. Hence Jesus said, don’t leave others in particular to the law which includes tithing undone.
A good analogy is like when you are about to replace a CEO of the company. The existing CEO have, say 1 month to clear his thing and you as the new CEO will commence working next month. Does the existing CEO still have the right to receive his compensation while he still remains to be the CEO, he does right? Same as the Levitical priest, Heb 8:4 says, Jesus will not overthrow the existing priest while he was still on earth, this is evident when He Himself while still on earth said, don’t leave others like giving the compensation for the Levites for doing their priestly duty undone.
One may say, well the new CEO when he commences work still need to receive compensation right? So does Jesus, since He is the new high priest replacing the Levites, tithing was therefore passed to Him. With this, I say, except for the obvious that Jesus is not physically present to collect His compensation as the high priest? If the new CEO is not available to collect his compensation, can it be collected by anyone? Or, the new CEO will need to issue some kind of authorization to collect what is for him right? So, since Jesus the new high priest is not available to collect physically, did Jesus authorized anyone to collect what belongs to Him?
Some would probably answer using the below verse:
“Here mortal men receive tithes, but there he receives them, of whom it is witnessed that he lives”. Hebrews 7:8
Implying that mortal men today can receive tithes but, apparently ALL men are mortal and the verse did not specify whose men. Actually, in the right context, the mortal men still refer to the Levitical priest as translated in AMP version:
“Furthermore, here [in the Levitical priesthood] tithes are received by men who are subject to death; while there [in the case of Melchizedek], they are received by one of whom it is testified that he lives [perpetually] ” Hebrews 7:8 Amplified Bible, Classic Edition (AMPC)
Note: Pardon me for wrong spelling and/or grammar.