I appreciate the long reply, but to me that first image you replied to looks marginal, and the one below is slightly after the ball is played. Alexander-Arnold is moving towards goal, and Nunes is moving away, so a couple of frames earlier could easily put Nunes offside (especially as he's running out quickly to try to get back onside).This is the point where Nunes is being judged for offside. This is confirmed in the ESPN article posted by @Bluehammer. Alexander-Arnold clearly plays Nunes onside. In fact from the linesman's position, there is no way he can see any Wolves player to the right of Alexander-Arnold, and he probably can't even see Nunes through that crown of players. To be certain of offside, there needs to be a Wolves player to the right of Alexander-Arnold, and there is not even a remote possibility of this. Hence it is not a marginal decision. Offside does not even factor in to the equation.
In this case, the ball being headed and the player adjudged to be offside are in a direct line from the linesman's vision. Alexander-Arnold is to the right of them. This is easy for the linesman to pick up. I've been a linesman at Maine Road, and this is not a difficult decision for a competent linesman.
This is a very specific incident, with a very suspicious set of circumstances. I would query this whoever benefitted, because it smacks of bias.
As referred to above, the article tries to give a balanced view of the incident. It says this:
"After the delivery into the box, the last attacking touch was by Hwang Hee-Chan -- this sets the offside phase."
This picture is when Hee-Chan heads the ball to Nunes, starting the attacking phase. (I appreciate this view wasn't available to VAR).
As I said, there is no way any competent linesman could have given offside in this situation, or anywhere else in this phase of play. This is why I think the decision is questionable.
I absolutely agree that there isn't any conclusive proof that Madley tells the linesman to raise his flag. But he is telling him something. Hence my question, what was said between the two of them.
The explanation we have been given is just not credible, and does not fit with what we see with our own eyes. If this evidence was presented in a court of law, the cross examination would be brutal, and Madley would be made to look a complete fool.
We don't have all the answers, but my money is firmly on trying to keep a high profile team in the competition. Imagine if Traore had scored the Salah goal, and Liverpool had a late winner disallowed in these circumstances. There would be questions in Parliament and PGMOL would have had to print a full page apology in the Liverpool Echo by now.
While you say everyone is in line, I can see what you mean, but it's not that simple. They are approximately in line, but the defender, the ball and the attacker are spread over nearly 40m, and the ball is yards to the left of the last defender. All three are moving in different directions. It's simply not possible for the human eye to track that accurately, hence why close offsides get called wrong all the time. Remember the movement from an offside position to an onside one, and the two headers, takes place in a fraction of a second.
It's a really tricky call for a human, and I bet if you went through all the VAR offside overturns so far this season, you'd find many similar decisions, which aren't being debated because VAR was working properly.