I should reiterate that I am obviously fully agreed that a father is the patriarchal head of his household, children should obey their parents, and even that arranged marriage is a very good idea. It is obviously a very good idea for a father to find a suitable husband for his daughter - that goes without saying in this company.
However,
@NVIII is exploring the far more controversial aspect of whether the father has the authority to compel his daughter to marry someone against her will. For that we need to examine the Law in far more careful detail, which I am doing - partly, to be honest, I am deliberately assuming an opposing position in the discussion to ensure it is thrashed out adequately and we don't just sit around agreeing with each other until we drift into error unwittingly. So, from that perspective:
Obviously, for a child, "honour your parents" basically translates to "obey your parents" in practical terms. And Ephesians 6:1 specifically says "child" - not "son" or "daughter" (which apply throughout life), the word fundamentally means somebody dependent on the parent, a young child. Literally Paul is saying that while young and dependant upon your parents (while a child) you must obey your parents. Paul is not telling adults to obey their parents (even if that is true, this verse does not say it).
Note too that this is not talking about daughters, but all children. If this verse applies to adults, then it also means that men must obey their parents.
@Bartato, honestly, do you obey your father? For instance, if he told you to never take a second wife, would you obey him? If the answer is "no", then you recognise that this verse does not apply to adults.
Honour does not always mean obey. To take the opposite extreme, you would honour your aged father with dementia by disobeying his orders to let him walk outside in the snow wearing only his pyjamas, and instead dragging him inside against his protests and warming him up. At this extreme end "honour" is no longer synonymous with "obey". At what point does this change? I would say "gradually".
This passage is very interesting as it gives the father veto power over the daughter's decisions. This is a very powerful authority - but also specific. It does not technically give the father the right to choose a husband for his daughter. If the daughter wants to marry Tom, her father can veto this decision. However, if the father wants her to marry Fred instead, but the daughter does not want to, where does the father stand? The father can approve or veto her decisions - but if she never makes the decision to marry Fred, he has no decision available to approve. This passage does not give him a way forward.
This passage gives the father very powerful authority over his daughter - all the authority he needs to prevent her from making bad decisions - but not unlimited authority.
Is there is another passage elsewhere that gives him the wider authority to compel her in this way? Or: