Offside question

I have confused myself over the offside rule. At a match on Saturday, where I was a coach rather than a ref, the midfielder played the ball towards a player who was in an offside position. The assistant referee flagged for offside just as the defender headed the ball out of play. The referee gave a throw-in as he said the ball did not reach the player who was in an offside position. At the time I thought this was the wrong call. But now I think maybe the ref was right, and have generally just confused myself. What's the right decision here?

The AR should not have signalled until the attacker became active by playing the ball (or interfering with an opponent's ability to do so)
Had the AR not flagged, the question would not have arisen, and the throw in would have been taken to restart play.
The referee was correct.

Clearly the the player in an offside position (PIOP) did not interfere with play but it's not entirely clear to me whether they might have interfered with an opponent.

It sounds like they probably didn't, but there's just not enough detail in your description to be completely sure. For instance, did they challenge the defender for the ball or clearly impact on the defender's ability to play the ball in some way? Again, not 100% apparent, based on the limited description.

Of course, if the PIOP did not interfere with an opponent in any of the ways set out in Law 11, then the referee was correct to award the throw in.

From the description this is what I have in my head.
An argument I hear all the time, at all levels of the game, and perpetuated by some referees/assistant referees is that the player somehow interferes by being in that position resulting in the defenders having to take action as they dont know it he's offside.
As we know it is not an offence to be in an offside position but this feels like the most likely confusion on this one.

Having read these comments, I am sure the ref was right that it was not offside. One bit of context I should have added is that that Assistant Referee was quite vigorous in his flagging, which influenced how I and others viewed it. Thanks for all the feedback.

Farncombe Pete said:

Having read these comments, I am sure the ref was right that it was not offside. One bit of context I should have added is that that Assistant Referee was quite vigorous in his flagging, which influenced how I and others viewed it. Thanks for all the feedback.

Click to expand...

Another error by the AR, as an offside indication should always be a vertical flag signal from an AR standing still.
Was the AR a neutral or club AR?

Club AR. It was an U14 Youth match. Perhaps highlights the importance of some simple pre-match instructions.

Farncombe Pete said:

Club AR. It was an U14 Youth match. Perhaps highlights the importance of some simple pre-match instructions.

Click to expand...

We don't expect club AR's to be as good as neutral/qualified assistants, and hoping they will act on pre-match instructions is often a vain hope, sadly. Many have "been doing this for years" and don't change, whatever is requested by the referee. A subtle art for the referee is the ability to manage those situations.